Some Premier League managers have called for a football-wide boycott of social media platforms to combat continued abuse and discrimination.
In addition, police are investigating racist and sexist comments sent to Liverpool winger Rinsola Babajide on Thursday.
A league-wide boycott will be discussed at next week's Premier League meeting.
The England women's Twitter account called on social media companies to "step it up" in response to the abuse directed at Babajide, which Liverpool have reported to the police.
Two years ago, a number of footballers took part in the #Enough campaign - a 24-hour social media boycott in protest at a similar spate of abuse.
However, there has been a recent increase in abusive messages being sent to players.
Liverpool players Trent Alexander-Arnold, Naby Keita and Sadio Mane were sent racist comments and emojis on Instagram after their Champions League defeat by Real Madrid earlier this week.
Reds boss Jurgen Klopp said it is a "big step in the right direction" for players to cut themselves off from social media.
"People can hide behind whatever account and say what they want to say, that's a problem and that has to get sorted on this planet as quickly as possible," he said.
"Abusers need a forum for that, they need a situation that you take these kinds of things seriously in, that's how bullying works.
"If you cut that side off that's already a lot done and it cannot harm you. That would be my advice to the players."
Aston Villa boss Dean Smith said the abuse is "getting out of hand" and called for a "blanket ban".
"There has to be a unilateral agreement between the clubs to boycott social media to see if we get some movement from the social media companies," he said.
"I think if the football clubs do it, the media should too. I would support it."
Newcastle manager Steve Bruce said he would "ban the whole lot" of social media if he could and that he was "right behind" the club boycotting it.
"The platforms should be policed and a bit like your telephone, you're accountable for what you do and what messages you send out there," he added.
Tottenham boss Jose Mourinho said only "the media giants" can resolve the problem and that "everything is in their hands to end this sad situation".
West Bromwich Albion contacted West Midlands Police earlier in April after striker Callum Robinson was targeted.
Manager Sam Allardyce wants to see "an accumulation of football clubs" boycott social media.
"That would for me be the only way that a difference may be made, if a united front was put up by all 92 professional clubs," he said.
"But if that meant losing revenue, the money may override that, unfortunately, because a lot of people are in a lot of trouble."
Facebook, which owns Instagram, responded to calls for a boycott by saying that it was committed to tackling abuse on its platforms.
A Facebook spokesperson said: "We don't want discriminatory abuse on Instagram or Facebook. We share the goal of tackling it and holding people who share it accountable.
"We're committed to our ongoing work with government, industry partners, and other experts to find the right solutions and collectively combat online abuse."
Swansea announced a week-long boycott from 8 April after several players were abused online. They were later followed by Rangers and Birmingham.
Liverpool captain Jordan Henderson has handed his Twitter account over to the Cybersmile charity to raise awareness of the impact of abuse.
Babajide revealed a racist comment she had received on Instagram.
"I wanted to speak up about it because I have stayed silent for so long," Babajide told BBC Sport.
"I just feel, as a black woman in this game, I am conditioned to it. It happens so regularly. It's more exhausting than anything. I've gone past the point of being disappointed or hurt by it."
Babajide said she immediately told her agent about the abuse and that he has yet to receive a response from the relevant social media platforms after contacting them.
In response to the racist abuse directed at Babajide, a spokesperson for Facebook said: "There is no place for discriminatory abuse on Instagram and this comment has been removed for breaking our rules."
Liverpool said in a statement: "This racist and sexist attack on LFC women's Rinsola Babajide has been formally reported to the police and an investigation is under way.
"Rinsola will continue to be offered our fullest support as well as that of the relevant authorities. LFC condemns all forms of discrimination and we reiterate - it is completely unnecessary and it has to stop."
Former Arsenal and France striker Thierry Henry last week removed himself from all social media because of racism and bullying across platforms.
What are companies doing?
One of the key problems is anonymity, with people feeling empowered to abuse players while hiding behind a screen name.
Some of football's governing bodies laid out the changes they would like to see in a letter to Facebook and Twitter in February.
They included filtering and blocking messages before they are sent if they contain racist or discriminatory material, and stopping people who had previously sent abuse from re-registering.
They also asked for an improved verification system to allow for "accurate identification" of the user if required by the police.
It would not be a solution that works for everyone - anonymity can be vital for people in other countries where social media bans are in place - but it would force trolls to take responsibility.
The UK government has threatened social media companies with "large fines" if they fail to tackle abuse on their platforms.
Fadzai Madzingira, Facebook's UK head of content policy, told BBC Sport in February it was introducing tougher measures, which included disabling accounts of those found to have repeatedly sent abusive private messages on Instagram.
However, it says asking users to provide verification documents would prove challenging in communities where such documents would not be readily available.