Brooks, who has won 21 Wales caps, was on international duty last month and credited the Wales medical team for helping detect the illness.
“The medical team will be in touch with David, I’ve not spoken to him personally,” Page added.
“He knows we are all fully behind him and fully supportive of him. He knows we are here for him.
“I can’t speak highly enough of our medical team for what they did and the support they gave Brooksy afterwards as it was a difficult thing to hear.
“The work they did that week was unbelievable.”
Wales enter their final qualifiers third in World Cup qualifying Group E, level on points with the Czech Republic who are second with a superior goal difference, but Wales have played one game fewer.
Page’s side will play both matches at home, with Belarus visiting Cardiff City Stadium on Saturday, 13 November, before Belgium, who have already won the group, visit the Welsh capital on Tuesday, 16 November.
Wales squad: Wayne Hennessey, Daniel Ward, Adam Davies, Chris Gunter, Ben Davies, Connor Roberts, Chris Mepham, Joe Rodon, Ben Cabango, Neco Williams, James Lawrence, Rhys Norrington-Davies, Aaron Ramsey, Joe Allen, Jonny Williams, Ethan Ampadu, Harry Wilson, Joe Morrell, Will Vaulks, Dylan Levitt, Sorba Thomas, Daniel James, Gareth Bale, Kieffer Moore, Tyler Roberts, Brennan Johnson, Rubin Colwill, Mark Harris.