Portsmouth and Hampshire police have begun investigations after some of the club's academy players allegedly used racially abusive language following England's Euro 2020 final defeat.
Images on social media purport to show a screengrab from a group chat from the club's under-18s side.
A series of racially offensive terms and images are used in it.
Marcus Rashford, Jadon Sancho and Bukayo Saka suffered racist abuse after missing penalties against Italy.
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England lost the penalty shootout 3-2 after the match finished 1-1 after extra time.
Hampshire Constabulary said it had received a report of a screenshot circulating on social media depicting discriminatory language in the early hours of Wednesday which was "being treated as a hate-related incident and is under investigation".
The force said it was working with the football club as part of their response.
"We will not tolerate hate crime in Portsmouth," a Hampshire police statement said. "Any crime perpetuated through ignorance, prejudice or hate is unacceptable."
Writing on Twitter, Portsmouth owner Michael Eisner said on Wednesday night: "There is no place for hatred or bigotry of any kind at Portsmouth FC or any other organisation with which I'm affiliated.
"We won't tolerate it, and there will be appropriate consequences for anyone who engages in racist behaviour in social media or elsewhere."
The abuse directed at the England players on social media led to widespread condemnation across the country.
England defender Tyrone Mings accused home secretary Priti Patel of pretending to be disgusted by the abuse suffered by the players, after she had previously described taking the knee as "gesture politics" at the start of the tournament.
Around 700 people attended an anti-racism demonstration at a mural of Rashford on Tuesday, a day after it had been daubed with racist graffiti.
"Portsmouth Football Club are aware of images circulating on social media that allegedly originate from an academy u18 group chat and which are discriminatory in nature," the club said in a statement.
"The club have launched an immediate investigation and will provide an update once this has been completed.
"Portsmouth Football Club strongly condemn racism and are totally committed to the elimination of all forms of discrimination. There is no place for it in our game or society as a whole."
It is the second investigation into players' conduct Portsmouth has had to carry out in the past two months.
In May, the League One club said some first-team players "fell below the standards expected of them" after an incident outside a nightclub following the final game of last season.
Pompey Supporters' Trust said it was "shocked and appalled at the news".
"We welcome the investigation by the club and following discussions with the club we are aware of the seriousness and urgency that this matter is being dealt with," the trust said in a statement.
"The PST is fiercely opposed to all forms of discrimination and abuse. These vile and abhorrent messages have no place in football or anywhere else in society."