The arrival of Chilean keeper Claudio Bravo from Barcelona on Thursday will push Hart further down the pecking order and is will probably signal the end of the 29-year-old's 10-year stay at City.
"No. Everybody is trying to improve. But I am not the type of manager to talk about players. Everybody will see what the squad is on August 31," Koeman told reporters on Thursday when asked if there was every any interest in Hart.
"There is no interest (in Hart). We have a game at Stoke on Saturday and that is more important than all the rumours. I need to prepare the team for Saturday."
Koeman said this month that his squad were only 70 percent fit after returning from a long holiday, and the Dutchman was still not entirely satisfied with the fitness levels of his players.
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"We are improving. We are close to 100 percent but I think some players did not get game time in pre-season. Maybe they need one or two weeks more to get everybody on the highest level," the former Southampton manager added.
Everton host Stoke City in the Premier League on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
