Patrick Stewart joined Rangers as chief executive in December after James Bisgrove stepped down from the role in the summer.
Chairman Fraser Thornton also took over from interim figurehead John Gilligan last month.
His arrival followed the publication of the club’s accounts for June, which showed a loss of £17.2m.
Clement was appointed in October 2023 and won the League Cup in his first few months.
However, he has failed to add to that, with Celtic strong favorites to secure a fourth successive Premiership title and a fourth successive domestic trophy.
Rangers – last year’s beaten finalists – begin their Scottish Cup campaign at home to Fraserburgh on Sunday, live on BBC One Scotland.
“I’m a winner and I always have been,” Clement added.
“When I was young, nobody believed that I would be a professional player and when I was a professional player, nobody believed that I would go to the national team.”
On the transfer, Clement indicated there was nothing to report on income and, on the possibility of an exit, said: “There are possibilities, yes, but we’ll see.”
Meanwhile, Leon Balogan and fellow defender James Tournier are back in training after recent absences.