Roberto De Zerbi said he wants in-demand midfielder Lucas Bergvall to stay at Tottenham, but cannot guarantee the Sweden World Cup player a starting role.
The 20-year-old reportedly wants to leave with interest from Newcastle and Nottingham Forest.
His future was cast into doubt by the recent arrivals of club-record signings Matheus Fernandes from West Ham and Sandro Tonali from Newcastle.
Spurs manager De Zerbi denied Bergvall had told him he was looking for an exit after starting him in the pre-season friendly against Sydney FC on Wednesday.
Tottenham won 4-2 on penalties after the match finished 1-1.
"I'm always being very clear with him and with you. I would like that he stays with us," De Zerbi said.
"I think he's potentially a top, top, player. But then I don't want to convince anyone to stay.
"Tottenham is already, without me, a top club and we are not to convince anyone to stay.
"I can't give, for any player in the world, a place in the first XI guaranteed."
French striker Mathys Tel scored a stunning free-kick to put Spurs 1-0 ahead at halftime against Sydney, but they failed to capitalise and the hosts' new Japanese signing Takahiro Sekine levelled.
Tottenham's shootout win came after a 2-0 victory over Auckland FC on Sunday as they build towards their English Premier League opener against Brentford on August 22.
"I think we played well, especially in the first half," he said.
"In the second half, we changed many players, but good quality of play, good performances and I think we are working very well with the younger players."
Tonali missed Tottenham's first tour game with a niggle, but played the entire second-half, while fellow new recruit Andy Robertson was given a 25-minute debut.
But there was no appearance from Fernandes, whose absence De Zerbi attributed to "just fatigue, in the calf, and also for him, we took the decision not to take any risks".
The Italian manager suggested Fernandes would also miss Tottenham's final tour match against Chelsea in Sydney on Saturday.
James Maddison was another absentee along with Kevin Danso, Destiny Udogie, Micky van de Ven, Jan Paul van Hecke and Dominic Solanke.
"Danso, van de Ven, Solanke, Jan Paul van Hecke, I thought they were not ready yet to play without risk," De Zerbi said.
"Maybe some of them can play the next game, on Saturday against Chelsea. Maybe not in the beginning, maybe at the beginning Robertson and Sandro Tonali.
"It is about managing the players. I wouldn't like to take any risks."