The Spaniard is expected to become the new manager of Wigan, where he spent six years as a player, on Wednesday, leaving the Swans managerless in what is an important time of the close season.
Martinez received plenty of plaudits for how he sent his Swansea side out to play and Jenkins was left feeling slightly
disappointed that the 35-year-old has decided to switch clubs.
But the Swans chairman knows the importance of selecting the right man to continue the good work started by his ex-manager and adds that a large percentage of the applicants are of a high standard.
"I have had about 100 enquiries already," he told Sky Sports News.
"Looking where we were three or four years ago it shows, with the number of applicants, that the profile has grown and it's going to be a very difficult job to replace Roberto.
"Out of those 100 enquiries I could easily have 30 on a list and
they're all top quality."
Jenkins pointed out that he would seek to have a new manager in place before pre-season, but confessed that a shortlist had not yet been whittled down.
"It's all about to get under way because the timing of it is not ideal," he stated.
"We have a few weeks left before the players are back in pre-season but we have not established a shortlist yet."
Coca Cola Ch'ship Promotion 09/10 Win Outright: Swansea 7/1