Martinez has brought Gerard Deulofeu and former Wigan trio Joel Robles, Antolin Alcaraz and Arouna Kone to the club this summer but would still be in the market for new faces.
However, the Spanish tactician revealed the form of teenagers Ross Barkley and John Stones has made him even more confident about the squad he already has.
"I've been very impressed with the youngsters," the former Wigan boss said.
"Ross Barkley and John Stones have really surprised me. I knew they had a fantastic future, but what they've got is a very special present, and that excites me.
"You always need to keep looking to try to help the players we've got at the club but we're not looking for a specific number. If we don't bring anyone in, I'll be happy."