Last week, the Croatian international expressed his frustration to local media regarding Southampton's decision to reject a £20m offer from Liverpool for the centre-back.
Lovren has admitted that he wants to make the move to Anfield by insisting that in his mind, he is already a Liverpool player.
Le Tissier gave his views on the situation by tweeting: "So @DejanLovren05 wants to leave Sfc for lfc cos were selling best players. If he signs & they sell Suarez will he want another transfer?
"IMO until your club accept a bid from a team wishing to buy you, the player in question should keep his trap shut.
"For the record I have no problems with Sfc players wanting to move on in their careers but don't throw toys out the pram to force a move."