Conway is due back at parent employers Cardiff City when his short-term loan agreement comes to a close.
The Scotland international has impressed during his time with the Seagulls and would appear to remain some way down the pecking order at Cardiff.
That means there could be a deal to be done in January, when the transfer window re-opens.
Barnes would like to see Conway brought back to the Amex Stadium, with the tricky winger having helped him to maintain his recent fine run of form.
He told The Argus: "Craig is a fantastic player.
"He has got great quality. He was at Cardiff and they didn't sign him for no reason. They got promoted and he was a big part of that last season.
"It would be great if he could stay but obviously it's about what he wants and what the clubs want."
Brighton's assistant head coach Nathan Jones has hinted that the issue of Conway's future will be addressed in the New Year.
He said: "He has got better in terms of productivity as his loan goes on and that is normal.
"It's sad he has got to go back because we would like to keep him but hopefully, God willing, it won't be the last we see of Craig Conway."