Rodgers was confirmed as the new Liverpool manager on Friday after a two-year stint with Swansea that saw him steer the Welsh club to promotion to the Premier League and secure their top-flight status with an impressive 11th-place finish last term.
There had been media speculation he would be interested in taking the likes of Joe Allen and Ashley Williams with him to Anfield.
But, according to Jenkins, he will have to wait until the end of next season before taking any of his old Swansea favourites to Merseyside.
"We have got some protection on Brendan coming back for our players in the initial period, which I think is the right thing," Jenkins told talkSPORT radio.
"He has got a timescale to assess things there and that is going to take him a while so I've got no worries there. We have got a 12-month respite."
In a separate interview, Jenkins told Sky Sports News that he was sad to see Rodgers leave the Liberty Stadium.
"We are obviously very, very disappointed that we lost Brendan but things move on," he said.
"I think that naturally he has got massive belief in his ability and he felt that if he was the right candidate, he would go forward."
He added: "We have got a good relationship, we have dealt with it in the right way with Brendan and Liverpool."
Swansea goalkeeper Michel Vorm, signed by Rodgers from Dutch club Utrecht before the start of the last Premier League season, said Liverpool had made the right decision but added it was tough for the Swans staff.
"I think it's the best move Liverpool can make," he said.
"I've worked with him for a year and he's the best manager I've worked with -- and I think he is the best manager maybe in the Premier League.
"He is quite young but very experienced and I think for Liverpool it's the best they could get.
"For him it's beautiful. For us it's the worst thing that could happen. It's disappointing but I think we showed throughout the season what we're capable of.
"If we can keep the club together we can go on playing good football under the new manager."
Swansea have yet to appoint a replacement.
Source: AFP
Source: AFP