Morecambe striker Redshaw was stunned to hear that medical tests had found 24-year-old Thompson, now with Tranmere, had contracted nodular sclerosing Hodgkin's disease last week.
The two know each other from their season together at Spotland in 2010/11 and Redshaw would like nothing more than to see Thompson back on a football pitch again once his six-month chemotherapy course is over.
"When I saw the news I was so upset," said Redshaw.
"He's just had a baby, a one-year-old baby girl, so it's obviously heart-breaking to hear.
"But I'm sure he's got the right family and friends around him. I just hope to see him recover well and to see him back hopefully playing one day."