Middlesbrough have rejected an offer of about £3m from a Middle Eastern club for record signing Afonso Alves.
The Teessiders were contacted by an unnamed side, understood to be from the United Arab Emirates, about the 28-year-old Brazil striker.
Manager Gareth Southgate said: "We have had a bid for Afonso but it wasn't something that we deemed to be acceptable.
"To be honest, it wasn't anywhere near what we would accept."
Alves joined Boro in January 2008 from Dutch side Heerenveen for a club record £12.7m, but has struggled to live up to expectations.
We have to accept we have players in the club who don't want necessarily to be here and how we deal with that is important
Middlesbrough boss Gareth Southgate
He scored only four league goals in 31 appearances last season as the club were relegated from the Premier League.
Alves is among a number of big-name players who are expected to leave the Riverside this summer as Boro prepare for life in the Championship.
The club have already lost Stewart Downing, who joined Aston Villa last week, and strikers Mido and Tuncay are also thought to be heading for the exit.
Speaking after Saturday's 3-0 friendly win at Macclesfield, Southgate insisted the club would use money from player sales to strengthen the squad.
"At some point we'll look to invest but we've got to see what the next few weeks bring," he told BBC Tees.
"We said at the start of pre-season we have to accept we have players in the club who don't want necessarily to be here and how we deal with that is important.
"In Downing, we've lost a player who was much liked by everyone in the dressing room.
"We wish him well, but we've got our own job to do."
Middlesbrough have already signed goalkeeper Danny Coyne and winger Mark Yeates this summer and Southgate now is likely to look at improving other areas of the team.
"The balance of the squad is still strong," he added.
"In terms of width, we've got Mark Yeates, Nathan Porritt, and Adam Johnson to come back in the next few games, plus Gary O'Neil who played in the middle, but we know he's very strong out wide.
"So we have quality in those areas and it's probably other areas we'll look to strengthen as we go forward."
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