Anfield side chase Man City pair as well as Crystal Palace winger and Schalke centre-back.
Liverpool boss Brendan Rodgers appears ready to stage a major squad re-shuffle this summer though the Northern Irishman is unlikely to be spending quite as freely as a year ago.
Rodgers spent over £100m on players last summer but the four target names by these sources indicate a more frugal approach.
The Daily Star claim that as well as Liverpool pushing to complete the long running free transfer signing of versatile England man James Milner the Merseyside outfit are also keen on bit-part player Stevan Jovetic.
The Montenegro international is valued at £16m and that may be a price Liverpool are willing to pay though they may elect to sell a striker before making such a move with the likes of Mario Balotelli, Rickie Lambert and Fabio Borini all battling for their Anfield futures.
Liverpool are also apparently keen on in-form Crystal Palace man Yannick Bolasie with the Daily Mirror claiming such a move could cost the club around £20m.
The same source believes that a move for Schalke defender Kyriakos Papadopoulos is also on the cards, the Greek international being out of contract in the summer and a useful addition to boost Rodgers’ defensive options.