Burnley will make an improved offer of £18m to West Brom for striker Jay Rodriguez later on Tuesday, Sky Sports News understands.
Clarets boss Sean Dyche is becoming increasingly frustrated by the situation and wants a new striker in before the transfer deadline on Thursday.
It is thought Rodriguez is keen on a move back to the Premier League with his hometown club, but is prepared to stay and try to get Albion back into the top division if a deal cannot be done.
Bournemouth, Newcastle and West Ham all made enquiries about Rodriguez earlier in the window, but it is thought the player prefers the option of returning for a second spell with the club he left in 2012.
So far, Albion have rebuffed two Burnley bids for the man who scored 11 times as the Baggies were relegated last season.
It is thought it would take a bid over £20m for Albion to be interested in selling.