Middlesbrough turned down a transfer request from England midfielder Stewart Downing on Monday.
"We received a written transfer request from Stewart this morning. It was considered before being rejected," chief executive Keith Lamb told the Premier League club's website.
"Prior to receiving the request we received an improved offer for Stewart from Tottenham [Hotspur]. We immediately rejected this offer and informed Tottenham that Stewart is not for sale."
Downing, who has 21 caps, joined Middlesbrough as a trainee in 2001 but has been at the centre of transfer speculation for several seasons.
Middlesbrough chairman Steve Gibson and manager Gareth Southgate said on Monday they would not be selling Downing or any other senior players as they face up to a possible relegation battle, having gone eight league games without a win.
"I have categorically told [Spurs chairman] Daniel Levy their interest is not welcome, nor will we entertain any further offers for Stewart," Gibson said.
"None of our senior players will be leaving the club this month."
Southgate said: "I'm not under any pressure to sell any player. In the situation we are in now we don't feel it would be right to let Stewart go."
Middlesbrough are one place above the relegation zone.
