But following a host of names being linked with the job and no action, Jenkins has broken his silence.
"I can confirm that we have made just three official approaches to different clubs about speaking to potential managerial candidates," he said.
"It would be unfair for me to confirm those candidates or clubs at the moment.
"Yes we've had disappointments, but I'm not surprised at the negative responses from the clubs we have approached; while perhaps sometimes when people are given the opportunity to become a number one they feel the timing isn't always right for them.
"I can assure our supporters that we are more than happy to pay compensation for the right man - and clubs are aware of that.
"While I'm mindful that the supporters would like to see someone in place as soon as possible, we will not make a rash decision by rushing into things.
"When we make an appointment, it has to be the right one.''
Sheffield United have twice blocked moves for permission to speak to ex-Wales captain Gary Speed who is on the coaching staff at Bramall Lane, while Hamilton Academicals boss Billy Reid has turned down the chance to speak to the Swans after an approach was made.
Of the potential candidates linked to the job, Graeme Jones became the latest name to be ruled out after after Wigan Athletic said the former Swans assistant manager would not be leaving the DW Stadium.
Exeter City's Paul Tisdale and Brighton manager Gus Poyet have both distanced themselves as has ex-Middlesbrough boss Gareth Southgate, while Bournemouth have warned the Swans off boss Eddie Howe.
It's getting a little worrisome that we don't have a manager so close to the season opener
nicewelshlumberjack
Scunthorpe United's Nigel Adkins has been named as one of the favourites, with Gianfranco Zola and Steve Clarke also briefly linked.
Former Reading and Watford manager Brendan Rodgers is emerging as one of the leading candidates according to two bookmakers.
But he told BBC Sport Wales: "It's obviously a fantastic job but at this stage, for me there's nothing to say."
Bristol Rovers boss Paul Trollope - one of the names mentioned by Jenkins as the type of manager his is looking for - is also creeping up the list, although Rovers say there has been no contact.
Jenkins urged the club's fans not to panic over the lack of activity.
"As a club we find ourselves in an unusual position," Jenkins told the
Swans website
. "Clubs who lose their manager are normally in disarray. We are not.
"We are lucky to have Colin Pascoe and Alan Curtis to hold the reigns, while you won't get a better captain than Garry Monk. They know how the club operates on a daily basis, having worked closely with the last two managers in Roberto Martinez and Paulo Sousa.
"This football club is sound and stable. It has a solid structure in place that we are determined to maintain rather than bring in someone new who wants to restructure the club and set it on a totally different path.
"That's why we cannot afford to make any rash decisions. We have to be selective and make the right appointment at the right time.
"Our overall structure has progressed a lot over the last three years and I am mindful of maintaining our principles, while also fully committed to finding someone who can work with us and take this football club forward again.
"I would urge our supporters to be patient and understanding because we are working extremely hard to do the very best for you and this football club.''
Source: BBC Sport
Source: BBC Sport