Lincoln handed former Norwich, Blackburn, Chelsea and Celtic striker Chris Sutton his first managerial job at the end of last month after parting company with Peter Jackson, and Fenty has not ruled out the possibility of the Mariners following suit.
"I wouldn't rule out an applicant looking to take their first steps on the management ladder such as Lincoln have done," Fenty told the Grimsby Telegraph. "We will look at every application but we have obviously tried managers with traditional approaches and it hasn't worked."
Fenty added: "The search for a new manager starts now and we will take our time. It may take two to three weeks but it is now about the future and not the past.
"Naturally, I'm sure there will be a raft of applications but I believe the team is in good hands with Neil Woods in temporary charge. I am 100% confident Neil is capable of doing the job."