The South Wales Evening Post reports that manager Garry Monk would like a relatively busy summer, and look to bring in six players in order to improve the side after their record-breaking Premier League season.
The report says a striker, a goalkeeper, a left-back and attacking midfielder are all on the club's shopping list, though Bafetimbi Gomis looks as if he will start next season as the main front man.
Jenkins is quoted as saying: "The transfer market is a tough one this year, tougher than ever I think.
"That is because as your squad of players develops and gets stronger, finding players who can come in and compete is more difficult.
"You aim to get players who are as good as if not better than what you have.
"That's more difficult than ever for us.
"Finding the players who can make the difference for us is going to be tough, but we have to make sure we continue to operate well in the market."
The nature of football is that in order to improve, even after a good season like Swansea have just had, they need players who can go into the starting XI and really make a positive difference.
After the sale of Wilfried Bony to Manchester City in the winter transfer window, they didn't stop putting in impressive performances and coming out with the results to match them, but it will be interesting to see how they do over the course of a season with Gomis leading the line. With the desire of another striker, will they be targeting someone on the prolific side, or just simply one who can contribute every now and again?
Ever since their promotion to the top-flight in 2011, they have been a side that has been able to control games, and hurt their opponents with dynamism and pace. Naturally any players brought in would have to fit in with that style and philosophy.
After a season when they managed to collect 56 points - finishing just four points behind the Europa League places - pushing for continental qualification will be a realistic target for them next season.
Jenkins is, however, right to suggest that acquiring players of the required quality will be no easy task, especially when working on a budget.