The seven-goal top scorer's representatives have been approached by three or four top-flight clubs during the current transfer window – but all of them are currently in the bottom half of the table.
Albion, plus Villa and QPR, are believed to be the interested parties.
Wolves are understood to have set a price threshold of around £2m-£2.5m for the 26-year-old, who is out of contract in the summer – but with a 'special rate' for arch-rivals Albion.
The club know they would risk a PR disaster by selling to their Black Country neighbours.
But Sako, who was used as a second-half substitute in Mali's 1-1 draw with Guinea last night, is understood to have told Wolves he wants to help them to promotion – because to play for the club in the Premier League is his "dream".
A source close to the player said: "I spoke to Bakary and he told me his priority. He is staying until the summer to try to get Wolves into the Premier League – that is his dream.
"Ideally, he wants to help Wolves to the Premier League, then he'd be the first to sign a new contract there.
"But if Wolves aren't in a position to go up at the end of the season then he will have the pick of three, four or five clubs in the summer.
"We have had contact from three or four Premier League clubs this month. But they're from places 12 to 19 in the Premier League and the risk is too big to take – they may go down to the Championship.
"I would imagine Jez Moxey (chief executive) would settle for 2.5m euros, although neither him or Kenny Jackett (head coach) want to sell, but Bakary will only go if it's a club in the top 10 of the Premier.
"But if Wolves are still in the Championship in the summer, then he will go."