He joined Leeds on a year's loan from PSG in the hope of winning a regular place, but after three games he has still not made a start and was not even on the bench against Southampton this week.
Domi, 25, had been expected to play at left-back against the Saints.
Instead, Reid decided to recall Ian Harte, but Domi said: "I am not someone who is going to make problems for the manager. I've told him I will work hard to get in the side and I am happy at Leeds."
He hopes to be in the squad for Saturday's visit to Middlesbrough. However, if Lucas Radebe recovers in time from the knee injury which kept him out on Tuesday, Dominic Matteo could revert to left-back.
Domi added: "When I was at Newcastle I enjoyed the derbies against Middlesbrough, so it would be good to play against them again.
"It will be a tough challenge because Boro have a lot of talent, including Mendieta and Juninho.
"Although we haven't won a game yet, we have been improving so maybe our first win will come at Middlesbrough. We should be higher in the table than 13th with the players we have."