The Italian's deal only runs until this summer, but he has made no secret of his desire to stay at the club having steered them to Premier League safety since arriving in January.
Saturday's 4-1 victory over West Ham United means that Swansea could still finish as high as ninth in the table, having been in the relegation zone when Guidolin was confirmed as manager.
"It's down to the chairman and down to the board to decide, but you can see things are working with him," Fabianski is quoted as saying by BBC Sport.
"We're playing well and picked ourselves up, not only points-wise, but playing-wise as well.
"We've improved the way we play because in the first half of the season we struggled a bit. You can clearly see that the work he has done has worked."
Swansea host Manchester City at the Liberty Stadium on Sunday in what could be Guidolin's final match in charge of the club.