On Friday the Sky Bet League One club revealed medical tests had found Thompson, 24, had contracted nodular sclerosing Hodgkin's disease and Moore is now hoping the support of his immediate family can help him beat the cancer.
Tranmere drew 1-1 with Preston on Saturday at Deepdale and supporters from both clubs observed a minute's applause in the seventh minute for Thompson, who wears the number seven shirt at Prenton Park.
"It was fantastic and we appreciate it," said Moore after the match.
"The crowd were brilliant when the Preston guys put the picture up on the board.
"He's got a hell of a fight on but he's a fighter. His wife was here and he's got a one-year-old daughter that will help him in his fight.
"It's one of those cancers where he's got a 90 per cent chance of beating it, but he's got a hell of a hard six months to come."
Former Rochdale midfielder Thompson was actually in attendance as Rovers moved out of the relegation zone with a point at North End, although he saw victory snatched away from his side when Joe Garner scored a stoppage-time leveller.
"Tommo was here; it was nice to see Tommo," added Moore. "It just would have been nice if we could have just held on for him."
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