The French midfielder has struggled for form since moving to Chelsea last summer and may welcome a return to the principality as a result.
Bakayoko signed a five-year deal with the Blues in July and has gone on to make 37 appearances in all competitions so far.
However, the 23-year-old has been left out of the starting eleven of late, amassing just two minutes of playing time in the Premier League since early February, with manager Antonio Conte losing faith in him.
Chelsea might be open to a sale this summer as a result and they’ll have adequate cover from Danny Drinkwater in his stead.
Monaco have struggled for form this season, finding themselves 14 points behind Paris Saint-Germain in the Ligue 1 table after 32 games.
Leonardo Jardim’s side have fared even worse in Europe, failing to win a Champions League outing this season, while conceding 16 goals in just six games.
The National say Monaco want the £110k-per-week outcast to provide a shield in front of their back four to stem the tide of goals and may have the money to meet any asking price.
Thomas Lemar could be on the move and his sale would give them a lot of money in the transfer kitty. Chelsea may have to brace themselves for a bid.
Stats from Transfermarkt.