Since moving to Anfield in 2014, Can has established himself as one of Liverpool's key men, but the German international has less than a year remaining on his contract.
That has led to interest in his signature from Juventus, who had hoped to sign Can during the most recent transfer window, but it appears that Liverpool may also have to try to fend off approaches from two Premier League rivals.
According to Tuttosport, Chelsea and United are planning to make a move for the 23-year-old before Liverpool offer the player increased terms to remain on Merseyside.
Both clubs are well stocked with players who can feature in the centre of midfield, but Can is seen as a player who possesses the quality to feature in either starting lineup.
During his time at Liverpool, Can has contributed 10 goals from 133 appearances in all competitions.