The Leicester City captain is preparing to come up against the Scottish Premiership side in a pre-season tournament.
The Championship pair both want to sign the 33-year-old.
Kolo Toure is set to reunite with Brendan Rodgers at Celtic.
The Italian side have proposed a loan deal with a permanent option to buy.
Moyes was confirmed as the new Sunderland manager on Saturday morning.
The Glasgow Rangers striker scored a goal on his debut against East Stirlingshire.
The Championship club have recently been the subject of a takeover.
The academy product could be on his way out of White Hart Lane.
The Scotland international enjoyed an excellent first season with the Championship club.
New Rangers signing Joe Dodoo made an instant impact on his debut.