The 26-year-old made his Blues debut during the stunning 3-0 victory over the Championship's automatic promotion chasers Derby County.
Tottenham Hotspur continue to build for the future.
The midfielder is a January signing from Ligue 1 side Bordeaux.
New Liverpool defender played for the Reds under-21s on Tuesday evening.
The Premier League trio all watched the Italian side's 1-0 victory over Verona earlier in the month.
The Premier League side are hopeful of getting their hands on Cook this month.
The Romanian has left the club for Watford.
The Gunners have already signed Mohamed Elneny from FC Basel.
A selection of the latest stories in the media involving Liverpool Football Club this Wednesday morning.
The Magpies are reportedly interested in signing the striker for a club record £18 million, but is he the right choice?
Spanish football expert Graham Hunter has suggested Manchester United are taking a leaf out of the book of Tottenham Hotspur in terms of dealing with Real Madrid.
The French international is what Spurs need to get into the Champions League.
The centre-back duo played the whole 90 minutes of Liverpool's 1-1 draw with Malaysia XI on their pre-season tour.