Some teams still have as many as 10 games remaining this season, but it appears that the relegation race is down to four clubs with 16th-place Swansea City eight points above the drop zone.
Aston Villa are also considerably off the pace, leaving Newcastle, Norwich and Sunderland to fight it out for 17th position, but Surman and Cook are split on who they think will remain in the division.
Surman thinks that his former side Norwich will edge out their rivals, adding that he feels they have been unlucky at key moments this season.
He said: "It is a shame to see them down there, but I think they have enough to get out of it. By all accounts, they have been pretty unlucky in a lot of games.
"They have played well but haven't been able to turn it into results. I'm keeping my fingers crossed that they will be able to get out of it."
As for Cook, he has suggested that the appointment of Rafael Benitez as manager of Newcastle could prove pivotal.
The defender said: "I think obviously with Benitez going to Newcastle, it's massive for the club. I would back them to stay up now. I'd say Sunderland and Norwich, but it's tough to call."
Until the start of the month, Bournemouth were considered to be in the mix for survival, but three successive victories have moved the Cherries as many as 13 points from safety.
They are not mathematically safe, but judging on years gone by, one more victory should make sure of their top-flight status for another 12 months.