West Ham are keen to sign Walcott for £20m.
But the England winger has told pals he has no desire to leave the club where he has spent the last 11 years.
That is despite Monaco ace Lemar having agreed terms with the Gunners.
A fee has yet to be finalised but it is likely to be around £35, with add-ons pushing that figure up by a further £10m.
Walcott did not have his best campaign last season and has found himself out of the England reckoning under new boss Gareth Southgate.
But he remains confident in his own ability and has been in a positive mood as arsenal players returned to training ahead of their pre-season tour of Australia and China.
French winger Lemar will prove a strong rival for Walcott. But the 28-year-old knows from past experience how his form can dip and rise.
He started last season well, scoring 11 goals before the turn of the year.
A Gunners source insisted Walcott was approaching the new season at the club in a upbeat frame of mind.
And although the Hammers would guarantee him first-team football, Walcott is determined to stay at the Emirates club to stake his claim in the side under Wenger.
