Lions boss Gary Rowett has already lost one assistant this summer after Callum Davidson was appointed St. Johnstone manager in June and Barrett is on Southend's shortlist, having made over 300 appearances for the Shrimpers as a player.
But asked if he was interested in the job, Barrett said: "No, I'm happy here. The gaffer has been brilliant with me since he's come through and ever since I walked into the football club, the club's been great. I'm learning all the time and it's great to work with someone else. I'm very, very happy here at Millwall and we're progressing nicely as well. I'm looking forward to being a part of that."
Millwall are just two points behind sixth-placed Cardiff ahead of Saturday's London derby at QPR and they will take their hopes of gatecrashing the Championship play-offs to the final day of the season with a third consecutive away win.
"It's game on, we're in the mix," Barrett said. "We're just got to make sure we keep getting results, it's like a shootout now."
