Rangers are playing in the Scottish Championship at the moment, while Celtic are currently in the Scottish Premiership.
The Blues drew 3-3 with Chelsea at the weekend in another disappointing late collapse.
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.