Fortune linked up with the Premier League's bottom club in January from Nancy and has scored three goals in 12 appearances.
A fee is in place for the deal to be made permanent, with Fortune yet to comment on whether he wants to stay at The Hawthorns in the event of relegation to the Championship.
Mowbray has praised the player's commitment to the Baggies' cause and is keen to hang on to Fortune in the long term.
Whole-hearted"Marc is well within his rights to keep his own counsel because I can't question anything he is doing on the field," said Fortune. "If I saw any signs of him stepping off the gas, he wouldn't be playing.
"But I see a very committed and very whole-hearted player giving everything for this club.
"Yes, he is a player we would like to keep if there could be a deal that could be done because his quality is very evident.
"We will wait and see. There is an agreed fee, but it is not locked in."