Grant retired as a Giant having not played in the NFL since they won the Super Bowl two years ago.
Coughlin led the tributes to the 34-year-old, whom he labelled "Mr Versatility" due to his ability to play well in a number of different positions.
"He did a great job when he was here. Mr Versatility. Played linebacker, played back in the secondary. We had a package basically designed to get him and others on the field at the same time and he responded very well," said Coughlin.
"[He was a] very smart player. A guy who can direct traffic, the guys respected him. He had an ability to recognize when things weren't championship quality. Guys respected him for that.
"I look forward to seeing Deon again and see if we can get him in here and talk to the team."
Grant's 11-year career also saw him play for the Carolina Panthers, Jacksonville Jaguars and Seattle Seahawks.