Antonio Conte and technical director Michael Emenalo have scouted Bakayoko twice this season, in Monaco's 2-1 win over Tottenham in November and the 5-3 loss to Manchester City in February.
Chelsea have long been tracking the France youngster, who recently rejected Monaco's offer to extend his contract beyond its 2019 expiry date.
However, in a blow to Chelsea's summer plans, Bakayoko's brother Soualio - who also acts as his agent - has underlined the 22-year-old desire to play for PSG.
"We've talked about it because Tiemoue is Parisian,' his agent, and brother, told RMC.
"When he was young, he wanted to go to PSG. He's always dreamed of moving there.
"When I asked him to imagine that he'd move to PSG one day, he told me 'I'd honestly like that. If they were to offer me a deal, I don't see why I would refuse it.'"