Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
QPR loanee Tom Carroll wants to "make it at Tottenham" but is prepared to consider all of his options at the end of the season.
The Latics lost key first-teamers such as Hugo Rodallega, Victor Moses and Mohamed Diame in the summer and have now slumped into the Premier League relegation zone.
But Martinez remains convinced he has the players to survive in the top flight if only his side can overcome their injury problems.
"What is affecting us far more in this period is that we've had injuries to seven or eight players," said the Spaniard, quoted in the Daily Mirror.
"In every transfer market where we have lost players, we have replaced them and improved the side.
"Victor Moses is a very special player, but his departure has helped us grow and invest."
Wigan have lost five of their last seven Premier League matches and face Arsenal at the DW Stadium on Saturday.