The 30-year-old midfielder has been linked with a return to the Premier League and both Bolton and Fulham have expressed their interest.
Reports says Fulham offered £2million plus a player for Greening.
West Brom chairman Jeremy Peace told the Birmingham Mail: “Contrary to reports this is the only offer we’ve received from Fulham.
“Jonathan is our captain and a vital member of the squad. Therefore we didn’t give Fulham’s offer a second thought.
“It is derisory for a player of Jonathan’s talent and experience.”
He added: “We made it abundantly clear at the end of last season that should any players leave then it will be on our terms.
“We want to keep all our best players as we strive for promotion back to the Premier League.
“We are under no financial pressure to sell anyone.”
