Gareth Southgate insists Middlesbrough have fielded no bids for either Stewart Downing or Jonathan Woodgate.
England winger Downing is a long-term target of Tottenham Hotspur, while Woodgate has been interesting former club Newcastle United.
Reports have claimed that Newcastle are ready to open talks to take Woodgate back to St James' Park before the close of the transfer window.
But Boro boss Southgate, who is also trying to add to his squad, says the club have received no offers for any players.
"It suggests to me we have got some good players," said Southgate in response to the rumours. "It doesn't annoy me because there is nothing you can do about it.
"Teams will speculate, teams might try to bid for your players - as yet, they haven't - but you get enquiries about your players all the time.
"In the end, we have the decisions and we have the say as to whether we decide to keep or sell players.
"It certainly doesn't annoy me. You look at your squad of players and if quite a few of them are attracting interest, that's a good sign, I would certainly say that.
"You look at certain other teams and say who would you take, and maybe there aren't too many.
"It certainly doesn't concern me at all.
"I am not under pressure to sell anybody and nobody leaves the club unless we think it is the right thing for the club.
"At the moment, we haven't had any bids for any of our players, so that makes life very easy."