The forward joined in a £25 million move from Newcastle United on Friday.
The midfielder insists he is not thinking about leaving the club.
Moyes was confirmed as Allardyce's replacement at Sunderland on Saturday.
The Leicester City captain is preparing to come up against the Scottish Premiership side in a pre-season tournament.
Kolo Toure is set to reunite with Brendan Rodgers at Celtic.
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.