Clyne had been sidelined for the majority of the campaign, down to third-choice at right-back after an injury-wrecked campaign last year.
Of late he returned to the fold, starting against Man United and making a further three appearances off the bench in December.
James Pearce of the Liverpool Echo confirmed the deal was done on Friday afternoon.
Liverpool have not, as yet, confirmed the move—but it remains something of a surprise to see Clyne leave after his recent involvement and his ability to cover at left-back.
Promising talent Rafa Camacho, who can also play right-back or down the wing, has also been the subject of an offer from Sporting CP at the start of January.
Although, 16-year-old Ki-Jana Hoever has been a regular at Melwood in the last month and could be seen as an option in a bold move from Klopp.
Clyne has played 103 times for the Reds since making his debut in 2015, scoring twice, and was an unused sub in the Champions League final last season.