Southgate said: "Clearly it's a really serious matter and it's developing very quickly".
Jack Wilshere is set to return to worldwide football for the first time in 18 months while Gary Cahill has been axed following his drop in form.
The England manager said that although Cahill remained in contention for a World Cup spot if he can regain his place at Chelsea, he felt it was prudent to assess Tarkowski and Mawson.
Tarkowski and Mawson have been rewarded for their solid performances at Burnley and Swansea respectively this season, while Bournemouth midfielder Cook has been called up for the second time after originally being drafted into the squad ahead of the 0-0 draw with Brazil in November.
Swansea City's Alfie Mawson is also included for the first time, along with Burnley defender James Tarkowski.
"Joe has had a hard period with his club and he had to miss out on selection a few times when David Moyes came in".
Burnley goalkeeper Pope has been called up after impressing for the Clarets, while Joe Hart retains his place in the squad as one of four goalkeepers.
"Jack's a player that has unquestionable talent". "The key for me is that he's playing in the games that matter for Arsenal and he's been playing well".
"He's got a great number of caps and he's the most experienced keeper in our squad so we wanted to keep him around".
And while some politicians have called for a full boycott of the event, Southgate said he was simply concentrating on his job.
"Always part of what I'm working on is the strength of the squad and people are able to come in", said Southgate.
An untimely knock means that Tottenham striker Harry Kane is among the notable absentees, with the man hoping to take the armband in Russian Federation this summer set to be sidelined until April with ankle ligament damage.