Fortune has been a shining light towards the end of the season for the Baggies and has attracted interest from several Premier League clubs including Fulham and Wolves.
But Mowbray has hope that the former Nancy talisman will stay put at The Hawthorns.
"There is hope. We have a good opportunity. He is a good man and the grass isn't always greener on the other side," Mowbray said in the Express and Star.
"He is at a club where his talents are appreciated and he knows he will play.
"If Premier League teams are after him, he could go and be a number three or four striker. It depends on what the boy wants to do."