The website added: "As of Saturday night, they were fighting to save his foot, which is at risk given the nature of the infection."
Giants spokesman Pat Hanlon said in a statement, "This is a serious situation that has been taken seriously from the beginning. We're all fighting for Daniel."
"My heart is with my brothers tonight," he wrote. "Get that W G-men. I love every one of you #thiswillnotdefeatme"
Giants coach Tom Coughlin gave a nod to Fells at Sunday night's post-game interview, following the team's 30-27 home victory at Metlife Stadium.
"We dedicated that game to Daniel Fells and his family and thank God we were able to give him a game ball," he said.
Later in the interview, Coughlin gave reporters the latest status on his player, who's also a father of two.
"Fells has had two very good days in a row," Coughlin said. "We walked into his hospital room Saturday morning at about 7:30, Ed Triggs and I. He was sitting up, his wife was sitting up and they both had a smile on their face. He had really had his first night of sleep for the whole week that night.
“Then he put two together and his MRI came back without any issues. Thank God and hopefully he will just continue in that direction and have this cleared up so he can go home and see his kids."
Fells could now lose his foot as a result of the MRSA, a contagious bacterial infection that is resistant to most antibiotics.
"In a locker room or gym, if you're sharing any towels or razors ... even lifting weights, you can come into contact with bacteria from somebody else."
The Giants have scrubbed their facilities, including their training and locker rooms, to avoid the risk of spreading the infection among other players.
Besser said the best way to prevent MRSA is to keep scrapes and cuts clean and covered.
And raised bumps that are accompanied by high fever should be brought to the attention of medical professionals, he said.