Jurgen Klopp's side swooped for £45m arrival Diogo Jota on Thursday, whilst at the same time agreeing to sell central defender Ki-Jana Hoever in the other direction for a fee of £10m.
It is understood that Liverpool will pay just 10% of the Jota transfer up front, leading to suggestions that another Red moving in the other direction would be the most optimum situation for both clubs.
And reports in the Daily Mail suggest that Nuno is keen on adding the player who, with the recent arrival of Thiago Alcantara, has moved even further down the pecking order at Anfield, with seven players now competing for just three starting berths.
Chamberlain made an excellent start to his career at Liverpool when signing from Arsenal but a serious knee ligament injury kept him out of action for more than a year and he has struggled to recover that form since.
Given the number of players in front of him now, he may want to ensure first-team football given he will be in Gareth Southgate's thoughts for his England squad ahead of Euro 2020 next summer.