The 27-year-old has yet to reveal who he will be joining when his contract expires, but regardless of that, Dutt is just pleased to have him in his squad for the next six matches.
"In sporting terms, we're really going to miss Aaron next year," Dutt said at a press conference.
"But you can tell that he would like an overall happy ending here. I have the feeling that his departure is not affecting him in the least.
"In fact, he seems to be putting his foot down for one last time. I was very happy with the way he played in Hannover.
"He was quick, ran a lot and just played the simple balls."
Dutt was also happy to see Aleksandar Ignjovski and Santiago Garcia training fully on Thursday, particularly in view of what they can expect to come up against.
"Schalke are very strong right now, particularly their attack," Dutt said.
Jens Keller's men have underlined that with four wins and a draw from their past five games, scoring 11 goals in the process and conceding just two.
"We're on a run," acknowledged Keller. "And we want to extend it in Bremen.
"It's important that we carry on picking up points and if we succeed in that, then we will qualify for the Champions League again."
The Royal Blues have already opened up a six-point advantage over fourth-placed Bayer Leverkusen in the search for a place in the Champions League group stage next season.
Two more wins could be enough to see them through, and Keller is to make it mathematically certain as soon as possible.
"Then we will be able to play without any pressure," added Keller, who welcomes Kevin-Prince Boateng back into his squad after suspension and has Kyriakos Papadopoulos fit again.