The Scottish international has been offered new terms by the club, as first reported by the Daily Echo, but is yet to sign the deal.
Che Adams, 27, currently has one year left on his Southampton contract and has scored three goals and provided an assist so far this season.
The forward was the subject of transfer interest during the summer window but remained at St Mary’s despite deadline day speculation.
Speaking ahead of Southampton’s away game against Middlesbrough, Martin said: “He got offered a new contract and it’s his prerogative.
“I’m quite relaxed about it as long as he gives everything he has got whilst he is here, which he does on the training pitch.
“He is a fantastic character like I’ve said before. If he gives everything he’s got on the pitch, it’s not a problem.
“Jason and Che’s representative will continue to keep talking, I’m sure, and we will see what comes of it.
“He was obviously in demand during the window and he didn’t go and he’s been brilliant about it.
“I’m pretty sure he just wants to hit the back of the net again. He was so frustrated with the chance the other night.
“It’s in his interest to do as well as he possibly can for us and in our interest that we kept him as well. He will be a big player for us.”