Doig has burst onto the scene in Scotland this season and interest in him is high ahead of the summer transfer window.
Watford are keen on the 19-year-old as the club have prioritised signing a new left-back.
They want to provide competition for Adam Masina and Doig is an option, although it is thought they may eventually opt for more experience.
Arsenal are also interested in Doig and have scouted him over the past 12 months as they search for someone to provided competition for Kieran Tierney.
Crystal Palace’s Tyrick Mitchell, as previously reported by Standard Sport, has also been watched this season but he is happy and settled after signing a new long-term contract at Selhurst Park.
Ryan Bertrand remains an option for the Gunners, with the left-back leaving Southampton at the end of this season when his deal expires.
Leicester City are long-term admirers of Bertrand and looked at him last summer when Ben Chilwell joined Chelsea.
They remain keen on the 31-year-old and they would be in pole position to sign him if they qualify for the Champions League this weekend.