Since being linked with the England post, Redknapp's side have lost third place in the Premier League and are now five points behind North London rivals Arsenal. They were also dumped out of the FA Cup semi-finals by Chelsea.
"Nobody has been talking about what we will do next season," Gallas said.
"His priority has been to get the team to qualify for the Champions League. So when the people start to speak about him for the national team he came to the dressing room and said: 'Guys, I am very focused on the Champions League and that's it'."
Parker backed Gallas's claims and said that the players and Redknapp are purely focussed on Tottenham.
Parker said: "It's probably a combination of a few things - a dip in form, a bit of tiredness.
"People are doubting us, whether that be our own fans, even our own manager probably at this moment in time is doubting us a little bit.
"We need to stand up and be counted for, and show the fans, and show him that we're going to try and end up fourth. If we don't end up fourth this year, we will have failed as a squad."
Tottenham travel to Queens Park Rangers on Saturday.