STV adds that the Light Blues will pay the same amount as the initial fee in 2017, while add-ons could also follow for the Lilywhites man.
The 31-year-old is on trial with the Light Blues, and the former Celtic loanee has been discussing the potential switch.
"If he is fit then he could be an asset to Rangers, but the key is fitness," he told the Express.
Dorus De Vries
The latter has become the Hoops' latest signing, and Rodgers has outlined how delighted he is to be working with him once again.
"I've been really, really disappointed twice in my career when I've lost players — one was Luis Suarez at Liverpool and the first one was Dorus de Vries at Swansea," he told The Scottish Sun.
The winger is still recovering from a hamstring injury, but is hoping to be back for the second-leg next week, The Scottish Sun adds.
The 20-year-old spent last season out on loan with Hibernian, but Rodgers has hinted that he could be a part of his plans by suggesting that he is a fan of Henderson.
"I've been talking to Liam about improving tactically. Technically he's very good and demands the ball which I love in a player," he told the Evening Times.
“I was disappointed but at the same time it was an opportunity to try something different. There was a lot going on at the club when it happened so it made it quite difficult," he told the Evening Times.