Rodgers missed the 1-0 defeat to Arsenal after his dad Malachy died at the age of 59 in the early hours of Saturday morning following a battle with cancer - a loss that came barely 18 months after the 38-year-old's mum Christina died of a heart attack.
But Rodgers is expected to return to Swansea on Wednesday following Monday's funeral, despite the club telling him to take as much time off as he needs.
Jenkins said: "Brendan has had a tough time personally over the last 18 months. But he is a special person who provides real strength for his family.
"He is a young man and things like this are a massive weight on anyone's shoulders. But he has coped with things remarkably well.
"He has something special about him and I think he's shown that with everything that has happened.
"Everyone within the club, together with our supporters, felt for Brendan on Saturday and our thoughts have remained with him and his family at this sad time.
"It puts football into perspective and we've told him he can take as much time as he requires.
"But knowing Brendan he will be back soon chomping at the bit. I spoke to Brendan on Sunday night and his last words to me were that he will return refocused and planning our success over the next nine or 10 months."