Guidolin opened the door for the two giants to swoop after he declared that he is uncertain if Ayew will stay with the Welsh club ahead of the start of the new English Premier League season.
The 26-year-old has been linked with moves to rival English Premier League sides Liverpool, Sunderland, West Ham and Chelsea.
Chelsea and Liverpool are thought to be the frontrunners in the race for the Ghana star following his excellent showing in his first season in England.
The Italian coach is desperate for the Ghana international to stay with the Swans but casts doubts over his future.
“Andre is a good guy and a good player, I hope he stays with us, but I don’t know,” Guidolin said in an interview with the BBC.
“It is important to keep him, but it is not my job,” he added.
“My job is to train and to get the team to play well and to get good results. I am confident he will stay.”
With the declaration by Guidolin, Liverpool and Chelsea are in pole position to start the fight to grab the Ghanaian star.
Ayew was a revelation at Swansea last season, and one of the few positives to come out of a disappointing campaign, as the Welsh side finished 12th.
The midfielder, who joined the club from French side Marseille, scored 12 goals in all competitions and was the club’s top scorer.
Ayew's future will be decided by the club's chairman Huw Jenkins, who is in charge of the club's transfer dealings.