Queens Park Rangers had wanted to sign Charly Musonda from Chelsea in the January window.
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.
West Ham United have reportedly been offered the chance to sign Al Ahli striker Moussa Sow.
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.