Cooper dedicated Tuesday night’s 1-0 win away at Hull City to Toby and said the club is “with him every step of the way.”
Five-year-old Toby, of Osmondthorpe, has battled stage four cancer Neuroblastoma since his fourth birthday, but was declared to be remission just months ago.
His family announced on Twitter last week that he has now been diagnosed with a brain tumour.
Toby’s family - backed by Leeds United -launched a campaign that raised the Â£200,000 needed to pay for antibody treatment.
However, over the last five weeks, Toby has been suffering from headaches and vomiting which had left doctors baffled, only for a CT scan on Friday to reveal that he now has a brain tumour.
Liam Cooper said after Tuesday night’s win: “Obviously everybody is devastated but we just want him to know that we are all with him, we are all rooting for him.
“He’s a terrific young boy and he’s done it before and he can do it again so we are all with him and that was one for Toby.
“I think we are just one big family and that’s the way the club should be.
“The club is renowned for that and we can all muck in and be strong by Toby because he’s the biggest fighter of us all.”
Cooper added: “It puts football into perspective when you hear the devastating news about Toby and we just want him to know we are with him every step of the way.”
United's players paid tribute to Toby by raising a shirt after the full-time whistle towards the away end that read 'Stay Strong Toby' following the latest news.
Toby’s mother, Stacey Worsley, has said doctors think the tumour is bigger than a golf ball and hope to start a course of chemotherapy in the next two weeks to try to shrink it.
She told the YEP: “We don’t think it’s spread anywhere else and so the doctors think there’s a better chance of reducing it in size.
"It may not clear but they’re saying they can try and shrink it down to basically nothing and it shouldn’t bother him.”
Toby seems “absolutely fine” in himself, Ms Worsley said. “You wouldn’t think anything was wrong with him.”
Support for the family has flooded in on social media, and Ms Worsley said: “We’re very grateful for all the love and prayers people are sending us on Twitter and Facebook.”