The New York Red Bulls forward is currently training with the Gunners for the MLS off-season.
The Toffees boss revealed that he approached the Frenchman before his side's 1-0 defeat at the Emirates Stadium on Saturday.
"I already asked him (Henry) on the way in. I asked him, he'll tell you; if he wants a game let me know," said Moyes.
Everton, who are currently 12th in the Premier League table, host Norwich City at Goodison Park on Saturday.