Sky Sports understands that West Ham have lodged a take-it-or-leave-it £10million bid for Matt Jarvis, but Wolves are refusing to discuss the matter.
The Hammers have already seen two approaches for the England international knocked back, but are refusing to give up in their efforts to lure the winger to Upton Park.
They have, however, made it clear that they will turn their attention elsewhere if their latest offer is rebuffed.
It is believed that the package put to Wolves includes £7m up front and £3m in add-ons, for a man who has handed in a transfer request.
Wolves are understandably reluctant to let Jarvis leave, with it their intention to keep their top talents on board for a Championship promotion push.
They have spent much of the summer fending off interest from Sunderland in Steven Fletcher, with several bids rejected.
It remains to be seen whether they can hang on to Fletcher and Jarvis, with manager Stale Solbakken aware that he will need to rebuild if two key men are allowed to move on.
"It's going to be a busy time before September 1," he said in the Express & Star.
"If we lose Fletcher and Jarvis, we have a job to do.
"You can't replace them at this level - if the ideal line-up included Kightly, Fletcher and Jarvis and it ends up without those three, we need to rebuild it, which can take time.
"I'm sure players will go and come in - maybe even before the Derby game."
Asked if Sunderland had been back in touch regarding Fletcher, Solbakken said: "If valuations are matched, something can happen.
"I don't know if the clubs are still talking."
Solbakken has also sought to play down reports suggesting Connor Wickham could be included in part of a deal to take Fletcher to Sunderland.
He said: "I've been in no contact whatsoever with this player.
"I want the transfer window closed now - can we do it at 12 o'clock?"