The Cameroonian defender has not played since 27 December and has missed a handful of games including the 0-0 draw against arch rivals Man Utd at the weekend, which saw Liverpool field a central defensive partnership of Jordan Henderson and Fabinho.
If Matip is deemed fit enough to play against Burnley, which is looking likely, then that will provide Henderson the opportunity to move back into his more favoured midfield position.
If the Liverpool captain moves higher up in the starting XI, expect Xherdan Shaqiri to be the man to make way.
Fabinho will probably continue at centre-back, though Klopp has youngsters Rhys Williams and Nathaniel Phillips to choose from if he wants the Brazilian back in midfield.
Shaqiri making way for Matip, with Henderson moving forward will signal the change back to Liverpool's usual 4-3-3 formation.
Curtis Jones is pushing for a start in midfield, but Klopp may save him for the FA Cup this weekend as the Premier League champions once again face Man Utd for the second Sunday in a row.
That means another start for Thiago, who was Liverpool's man of the match against United.
The Spaniard dominated proceedings at Anfield, earning a 9.2 FC Rating for his performance.
Virgil van Dijk, Diogo Jota, Naby Keita, Joe Gomez, and Kostas Tsimikas remain absentees.