There have been conflicting reports regarding the stance of the American owners, with The Times recently claiming that they are reluctant to sack Guidolin if the players and fans are willing to be patient.
According to talkSPORT, senior figures at the Liberty Stadium have given up hope and Guidolin could be out the exit door in the next few days.
The 60-year-old signed a two-year contract in the summer after helping Swansea stave off the threat of relegation following his arrival in January last season.
The Italian has suffered four defeats and recorded a draw in the Premier League since the team’s opening-day victory over Burnley
Manchester United legend Ryan Giggs has reportedly already spoken to the club regarding the managerial situation.