The Italian is reportedly fighting for his job with Ryan Giggs the main contender to replace him as Swans boss.
Swansea City manager Francesco Guidolin says he is not feeling any pressure at the Liberty Stadium, despite rumours suggesting the former Udinese manager is fighting to save his job according to BBC Sport.
The Italian saw his Swans side lose 2-1 to Manchester City in the EFL Cup on Wednesday, continuing a miserable run of four games without a win and just two wins in seven since the start of the season.
Guidolin has been dogged by rumours of player discontent with high profile spats between Neil Taylor and Ki Seung-yueng and The Telegraph claims sources have described the 60-year-old as a 'dead man walking.'
Speaking after Swansea's midweek defeat, Guidolin brushed off any speculation about his job saying: "I know football is like this, there's no pressure for me, it's my job", according to BBC Sport.
"We played with aggression and intensity, good ball possession but it's not a good moment. We have to look forward and if we play well and we work hard I think it will improve."
The Telegraph reports that former Manchester United assistant manager Ryan Giggs is chairman Huw Jenkins' preferred choice to replace Guidolin and change could happen as soon as October before the international break.
Swansea's new American owners are thought to have blocked Jenkins' desire to axe Guidolin as they are reluctant to make a change so early on in the season.
Guidolin's relationship with his squad has rapidly deteriorated and his methods have left a lot to be desired, with The Telegraph alleging he missed some of Swansea's morning training sessions on their pre-season of the United States to watch the Tour de France.
The former Parma coach took charge of Swansea in January with the club just two points above the relegation zone and steered them to safety and a 13th place finish last season, subsequently being rewarded by Jenkins with a new two-year contract.
But with his future now suddenly uncertain, Wales manager Chris Coleman has also entered the frame to replace Guidolin at his hometown club where he spent four years from 1987 to 1991.
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