The Baggies are believed to have offered £5million but it is understood Forest have told Albion the winger is not for sale.
The Reds value the 25-year-old much higher but, while they adhere to the conditions of breaking Financial Fair Play rules, would be unable to spend the proceeds from any sale.
West Brom boss Tony Pulis is on the hunt for wide players and has already signed Wigan’s James McClean for £1.5million this summer and has been linked with QPR’s Matt Phillips.
They were interested in Wolves’ winger Bakary Sako but baulked at his wage demands and are not expected to revive their interest.
The Baggies’ transfer plans are expected to step up a gear once Pulis returns from America with the squad next week, the Baggies lost 3-1 to Orlando City last night.
Antonio has been a long-term target for Pulis but Forest chairman Fawaz Al Hasawi last week said that the Sky Bet Championship club had no intention of cashing in.
He said on Twitter: “I would like to reassure our fans that I have no intention of selling Michail Antonio or any other player who wants to be part of this club.”
Antonio started every Sky Bet Championship game last season and scored 15 goals during an impressive first campaign at the City Ground following his arrival from Sheffield Wednesday for £1.5million.