Monk confirmed on Friday that he had opened preliminary talks with Swansea over extending the three-year deal he signed last May.
The 36-year-old - the youngest manager in the Barclays Premier League - has had a memorable first full season in charge at the Liberty Stadium as Swansea have recorded their highest finish of eighth with a club record points total.
Monk has been linked to both Sunderland and West Ham but Jenkins says a new deal is about rewarding the former Swansea captain for what he has achieved rather than fending off interest from rival clubs.
"First and foremost it's about reward to show Garry what we think of him, and he's there leading us to make sure we remain in the Premier League year on year," Jenkins told BBC Wales.
"I think we'll find a solution very quickly, we've got a good relationship with Garry and we'll find some way of working things out that he is rewarded in the right way.
"While we like protection, I think the ultimate thing with us is whoever the manager is has to want to stay and work with our football club.
"If they don't they'll move on..
whether it's the manager or players, once I see they don't want to be at our football club they won't be here long.
"That will always be in our nature."
Jenkins said he hopes Monk stays as manager far longer than the two years Roberto Martinez and Brendan Rodgers spent in the hot-seat, but he accepts other clubs will come calling if Swansea are successful.
"With every appointment you always keep your fingers crossed and hope things work out," Jenkins said.
"But you've got to try and make sure the personality is right at the right time because the club needs certain things at certain times.
"Garry stepped in last year, finished the season strong for us and he's had a fantastic year.
"He's brought the squad of players together and you can see they've got a good collective motivation and commitment for the football club.
"He's done all we thought Garry could do - and more
He's done a remarkable job.
"Garry is new to it and let's hope he spends more than the two years Roberto and Brendan did with us.
"But let's not forget that clubs in the Premier League and around Europe are always looking for young and up-and-coming talent, players and managers.
"We've got to accept it and perhaps realise we've got to contend with that because of our success."
Martinez took Swansea into the Championship while introducing the passing philosophy that the club have become renowned for.
The Spaniard left for Wigan in the summer of 2009 but, two years later, Rodgers' first season in charge ended with Swansea becoming the first Welsh club to be promoted into the Premier League.
Rodgers left to become Liverpool manager and almost won the title in his second season at Anfield, while Martinez is now also on Merseyside at Everton with an FA Cup triumph on his CV from his Wigan days.
But Jenkins had no hesitation in naming Monk as the best manager Swansea have had.
"He has to be (the best), he's finished with the top number of points and finished eighth in the Premier League," Jenkins said.
"You can't argue this year, I can't say anything different.
"Garry has grown and developed as a person, as a manager and learnt a lot in this period, and I feel he's finished the season in a real strong, positive way himself.
"We've had a fantastic season..
many targets were broken.
"Many things have been a first for us but that just highlights what a great season Garry, his staff and the players have had with his first full season in charge as manager."
Source : PA
Source: PA