The Italian club are setting their asking price at approximately €80m for a player they signed for just €18m last summer from Dinamo Zagreb.
Gianluca Di Marzio reported the two Premier League approaches, with Portuguese journalist Pedro Almeida identifying Tottenham Hotspur as one of the bidding clubs.
Bayern Munich have also been linked, though are understood to be pursuing Ismael Saibari as the primary offensive midfield target — and signing both Saibari and Baturina in the same window is considered unrealistic given Bayern's simultaneous work on the Nathaniel Brown left-back deal.
Baturina scored eight goals and provided four assists in 34 competitive appearances as Como qualified for the Champions League for the first time in their history — an achievement in which he was a significant contributor.
The 23-year-old's technical quality and his ability to link play in tight spaces between the lines have drawn admiring assessments from across Europe.
Como's position is clear. They have no financial pressure to sell, are retaining Baturina for their Champions League debut, and will only engage in serious talks at €80m or above.