The 25-year-old had a successful loan spell at the Portuguese club last season.
The 25-year-old’s two Carabao Cup appearances for the Reds last autumn were his first for the club since December 2017 before he moved to the Estadio do Dragao.
Grujic has spent the majority of his five years at Liverpool on loan to Cardiff, Hertha Berlin and Porto and the club are happy to offload him this summer.
The PA news agency understands the Portuguese club are favourites to sign him as they have been talking to the Reds about a permanent deal for some time.
However, they are believed to have to sell in order to buy and that may open the door to interest from clubs in Germany and Italy.
Back-up goalkeeper Adrian is staying at Anfield, however, after signing a contract extension.
The Spaniard made just six appearances last season, including the disastrous 7-2 defeat by Aston Villa, and fell behind Caoimhin Kelleher in the pecking order to be Alisson Becker’s deputy.
Nevertheless the 34-year-old is happy to remain.
“It’s a reward from the club for the hard work that I’ve been doing since I signed two years ago,” he told liverpoolfc.com.
“I really appreciate that confidence from the club, from the manager and from everyone involved in that situation.
“And secondly, and above all of that, it’s a pleasure to stay in Liverpool – it’s such a big club… it’s very special for any player to stay here. I am privileged.”