Suh is entering the final year of his current deal and is expected to negotiate a lucrative extension having established himself as one of the team's most valuable players.
Mayhew revealed that there was a desire on both sides to agree a long-term deal, and said that it was now simply a matter of when it would happen.
"I think that's going to be something that we certainly like the way that he's playing, like to have Ndamukong around," Mayhew told reporters.
"He's expressed that he wants to be here in the long term, so I think there's a time frame that might get done, but I don't know when that's going to be.
"If it's going to be sometime before the start of the league year, sometime during the league year, sometime during the fall - but there certainly will be an effort made to try to get that done, try to get an extension done long term."
Suh made 49 tackles and 5.5 sacks this season to earn his place in the Pro Bowl for a third time.