Murray Davidson is set to earn a new deal with St Johnstone.
The Perth midfielder continued his comeback from a long-term knee injury by playing 70 minutes against Ross County’s under-20s on Tuesday night.
The Scotland international has been out for eight months after snapping his patella tendon and signed a short-term contract in the summer which runs out at the end of the month.
But Wright has now seen enough from the 26-year-old to open up discussions on a longer deal.
He said: “Murray did well the other night in the under-20s. He played for 70 minutes but you can see he’s still short of full match fitness.
“That’s what we expected, though, because he’s still recovering from his injury but he’s not that far away.
“He’s already two months ahead of schedule so he’s done really well to get to where he is right now.
“I’m more than happy with him and the way he’s coming along. The chairman and I had meetings with him and his advisers on Tuesday so we’re hoping to get him tied up on a longer deal.”