Bakayoko has been strongly linked with a switch to Premier League champions Chelsea this summer, although reports last week suggested that United had entered the race for his signature.
However, the Manchester Evening News claims that Mourinho has instead made Tottenham Hotspur's Eric Dier and Chelsea midfielder Nemanja Matic his transfer priorities in that position due to their existing experience in the English top flight.
Mourinho brought Matic back to Stamford Bridge during his time in charge of Chelsea, while the latest reports suggest that the Red Devils are willing to spend up to £60m to prise Dier away from White Hart Lane.
Both are understood to be seen as viable options for Mourinho, who wants to bring in a holding midfielder as a long-term successor for new club captainMichael Carrick.
The United boss has also reportedly ruled out a move for Bakayoko's Monaco teammate Fabinho for similar reasons.