Robson, 74, was invited to the Toon's training ground where he talked to players and coaches.
"Bobby is not so well at the moment but it was good to have the opportunity to speak with him.
"He has been around the training ground for a few chats.
"A lot of people have worked here for a long time, so they know him and were really pleased to see him."
During his first season in charge of Bolton, Allardyce received some advice after he was beaten by Robson's Newcastle.
Allardyce added: "He said it was important to have a positive attitude and not to let it affect the confidence of the team.
"That's more or less what he was saying today.
"He told me it's not an easy club to manage - but a great club if you get it right."