Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
Chelsea striker Fernando Torres is understood to be set for a return to Atletico Madrid, according to Sky sources.
The 19-year-old has arrived at Molineux to provide competition at left-back with George Elokobi injured and Stephen Ward the only remaining option in the position.
Robinson, who is an England U21 international, could go straight into the Wolves squad for Tuesday's crucial Championship clash with Barnsley.
Wanderers boss Dean Saunders said: "We've got no cover in that position with only Wardy at the club and he was ill yesterday so I've acted quickly and got the deal done. I think Wardy will be OK for tomorrow, though.
"Jack has played for Liverpool this season and he's going to be a good player when he comes of age. He is aggressive and he's going to come and help us."
Robinson became Liverpool's youngest ever player when making his Premier League debut against Hull in 2010 but has failed to establish himself at Anfield since with the likes of Jose Enrique and Glen Johnson ahead of him in the pecking order.