Saka, 18, is a rising star in Mikel Arteta’s squad, but has entered the final 18 months of his current deal.
The Daily Mail claim United and Liverpool are monitoring Saka and his ongoing contract talks with Arsenal.
As a result, Arsenal will try and tie Saka down to a new long-term deal as soon as possible.
Saka is on a £3000-a-week contract and could be in line for a healthy wage boost in a new deal.
Bayern Munich are also tracking Saka, who has made 15 appearances in the Premier League this season.
Unai Emery was the original coach to promote Saka to the first-team squad and Arteta is expected to give the youngster even more game time in the final half of the season.
Saka has played at left-back for Arsenal this season due to injuries to Kieran Tierney and Sead Kolasinac, but is naturally a left-sided attacker.
Arteta has already singled out Saka for praise since taking charge at Arsenal and the player has been impressed with his new coach.