MILAN (Reuters) - Inter Milan still need a midfielder and the door remains open for Frank Lampard, coach Jose Mourinho said on Wednesday.

Mourinho won two Premier League titles with Lampard while at Chelsea and has had a bid rejected by the club, who say they will not enter into negotiations over a transfer.

Media reports have said Lampard is torn over whether he should move to Italy and Mourinho is willing to wait.

"The transfer window is open until August 31 and we need a midfielder. Lampard is at Chelsea, but I have worked really well with him," Mourinho told a news conference on Inter's first day back for pre-season training.

"I worked with Frank for three and a half years, there is an unforgettable relationship. But in this moment I respect players and the clubs."

The Portuguese coach, who left Chelsea last September, took over Italian champions Inter in June after Roberto Mancini's sacking.

Mourinho also has his eye on compatriot Ricardo Quaresma but wants to sort out a bulging squad first.

"I like Quaresma, but he is at Porto. Anyway, the squad needs trimming. I want to work with 22 players at most, plus the goalkeepers," Mourinho said.

The coach had words of wisdom for Brazilian striker Adriano, who has returned to Inter after recovering his form and fitness on loan at Sao Paolo.

Adriano earlier arrived at Inter's training ground saying he would give his all and score lots of goals.

"The words I've heard are positive," Mourinho said. "But tomorrow I want to see him really tired after the first training session."

The charismatic Mourinho, who said he was pleased AC Milan had bought Ronaldinho because it reflected well on Serie A, also warned his new troops as a whole.

"If I arrive at training an hour and half early I cannot accept it if someone arrives late," he growled.

"Fines are not important but if I say 10 then training starts at 10. If there are only 14 players, I'll coach the 14. The others can go home and stay there also on Sundays."

(Writing by Mark Meadows, editing by Rex Gowar)