The team still is figuring out how long Cook will be sidelined, and an indication will come from whether it places him on injured reserve, which would sideline him a minimum of three weeks, according to the source.
Cook was carted off the field late in the third quarter and ruled out for the remainder of the game.
Coach Mike Zimmer did not have an update on Cook's condition following the Vikings' 34-26 loss to the 49ers but said the running back would undergo an MRI on Monday.
Cook was injured after being brought down by Niners defensive tackle Kevin Givens following a handoff. The running back lost the ball in the process of being tackled and immediately grabbed for his chest with his right arm when he hit the ground.
He remained down on the field for several minutes as athletic trainers tended to him. Both Vikings and Niners players knelt around Cook while he was moved onto a cart before being taken off the field and back into the locker room for further evaluation.
Cook's day ended with 10 carries for 39 yards and six receptions for 64 yards. He was replaced by backup running back Alexander Mattison, who rushed three times for 8 yards and caught one pass for 2 yards after Cook left.
Information from ESPN's Courtney Cronin was used in this report