Swansea manager Francesco Guidolin says he feels no pressure after defeat by Manchester City.
The Swans were knocked out of the EFL Cup on Wednesday and are 15th in the Premier League with just one win in five games.
Reports say former Wales captain Ryan Giggs and national coach Chris Coleman are potential replacements if the 60-year-old Italian were to leave.
"I know football is like this, there's no pressure for me," said Guidolin.
"It's my job. I know my job."
Guidolin's Swans have a tough run of fixtures, starting with another home game against leaders City in the Premier League on Saturday, Liverpool at home on 1 October then Arsenal away after the international break on 15 October.
Swansea were acquired by an American consortium headed by Jason Levien and Steve Kaplan in July this year, but long-serving Huw Jenkins remained as chairman.
It is expected any decision to change the team management would have to be agreed by the owners and Jenkins.
Guidolin said his team were better against Pep Guardiola's than they were when losing 1-0 at Southampton on Saturday.
"We played with aggression and intensity, good ball possession but it's not a good moment," he said.
"We have to look forward and if we play well and we work hard, I think it will improve."
Earlier this week, Swansea midfielder Leon Britton called on his fellow players to show Guidolin "respect" following outbursts of dissent from Neil Taylor and Ki Sung-yueng after being substituted.
Britton, 34, returned to the side for the first time in a month to face City on Wednesday and earned praise from his manager for his performance.
"Leon Britton played a very important game," said Guidolin, who was awarded a two-year contract in May.
"But for Saturday we have to see. There is not a lot of time to take a rest but we have to be ready for Saturday. We can play another good game."
Pick your final Premier League table
There are 18 rounds of games left in the Premier League but how will the table look when the season finishes? Will Chelsea remain on top? Will Hull still be stuck at the bottom? Pick how you think it will look at the end, placing all 20 teams in order. Have a go then share with your friends.