The former defender took over from Michael Laudrup in February and has guided the team to 12th place in the Premier League table after four wins, three draws and five defeats in his 12 league matches in charge.
With their top-flight status now assured for another season, Monk revealed on Thursday that he has held talks with Jenkins regarding his performance this season, as well as his future ahead of next term.
"I have spoken to the chairman," he said. "It was a review of what I have done this season and stuff like that. Going forward, how I feel about things and what I would do.
"I think it's natural you would have that chat, and I think the chairman took it on board.
"I think there is a board meeting planned before the end of the season when they will chat and discuss things and make a decision before the end of the season.
"Of course I am hopeful (of getting the job). It is something I really enjoy doing, I've learnt a hell of a lot in a short space of time, and once you get a taste of it, you don't want to let it go.
"I trust the board and the chairman and everyone that they will make the right decision for the club."
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