Grant made a crucial contribution for The Baggies over the Christmas period when on a month's loan, giving Albion the bite in midfield they have been missing since captain Derek McInnes was struck down with injury in October.
Albion's bid is believed to be close to Joe Royle's asking price and are confident they can bring Grant to The Hawthorns permanently, although two unnamed First Division clubs are interested in the player.
"We've made an offer for him and Manchester City are considering it," Baggies chief executive John Wile said.
Meanwhile, Lee Hughes' link-up with agent Tony Stephens' SFX Group - which also includes such luminaries as Michael Owen, David Beckham and Roy Keane - has led to speculation that he may be moving from his boyhood idols.
Hughes' former agent, Dale Wright, said the two parted on good terms.
"We both left GP Management for different reasons at around the same time," Wright said.
"Lee is at a critical point of his career and I know he is destined for the top. Tony has inherited a potentially world-class player in a terrific position professionally. I know he is in very good hands. Lee remains a very close friend and I wish him all the success he deserves."
Albion have always insisted that Hughes, the joint top scorer in the First Division, will not be allowed to leave The Hawthorns but, despite his loyalty to The Baggies' cause, if they fail to win promotion this season he may decide that at the end of the season - at the age of 25 - it may be time to test himself at the top level.
