The Mail on Sunday says Tambling, 71, has been in hospital for four months battling Martorelli's Ulcer, a painful disease involving leg ulcerations.
Lampard grabbed his double century for the European champions in a 2-0 win over his former club West Ham United in the Premier League last Sunday and after the game he phoned ex-England forward Tambling to offer encouragement and support.
"It was so thoughtful of Frank to take the time to speak to Bobby," Tambling's wife, Val, said.
"They were talking for about 20 minutes. He said Frank couldn't have been nicer to him. He told him to stay positive, to take his time and he would get better.
"Bobby has the greatest respect for Frank and says he is one of Chelsea's greatest ever players."