Albeit known for some time, the centre-back's eight-year stint at Anfield officially came to an end in June when his contract was allowed to expire.
On the back of having not featured since December due to a serious knee injury, Matip has been in no rush to commit his future to a new club.
Furthermore, there has not necessarily been a desire for any teams to make an immediate move for the ex-Cameroon international, despite the expectation that there will be fierce competition for his signature.
However, now that the summer transfer window has closed and clubs are aware of how many slots that they have available in their respective squads, interest is likely to ram up.
Clubs join West Ham in tracking Matip
West Ham United have allegedly already made their move for the 33-year-old given the lack of strength-in-depth in that area of the pitch.
As it stands, though, Julen Lopetegui is yet to give the green light to pull the trigger for the veteran, leaving the door open to their Premier League rivals.
According to The Mirror, Fulham and Bournemouth are also monitoring any developments with Matip's future.
The report suggests that progression with any of the three clubs could be dependent on there being a willingness to hand Matip his desired two-year deal.
While clubs from outside of England's top flight are said to be admirers, it is alleged that Matip's preference is to stay in a league that he has played in since 2016.
Which club would be the best fit?
At this stage of his career, Matip will realistically have to choose whether he wants to be a squad option at a big club or first choice at a team with a lower profile.
Having added Joachim Andersen and Jorge Cuenca to their ranks, Fulham are well stocked for options in the centre of defence, Matip theoretically starting with four players ahead of him in the pecking order.
Meanwhile, at Bournemouth, Ilya Zabarnyi, Marcos Senesi and Dean Huijsen are the established trio at the top of the list of options available to Andoni Iraola.
With none of the three above the age of 27, Matip would offer a more experienced option to the Spaniard should he want to make the switch to the Vitality Stadium.