"There's a lot of work to be done and we have a shortlist in our minds," Jenkins told BBC Sport Wales.
"We haven't approached anyone yet. we are going to take a couple of days to see who is coming into the frame."
Jenkins says he has received between 30 and 50 applications for the Liberty Stadium post since Sousa left by mutual consent on Sunday after just one year in charge, and the Championship club "hope to get someone by the weekend".
Exeter City boss Paul Tisdale and Scunthorpe United's Nigel Adkins have been touted as the frontrunners, but both have distanced themselves from the speculation.
Tisdale, 37, reportedly turned down the Swans last summer when they were looking to fill the void left by Roberto Martinez who left for Wigan Athletic.
It is understood the Swans are still interested in Tisdale and Exeter opened the door for a move on Wednesday, saying they would not stand in Tisdale's way if he wanted to leave.
Tisdale has got far more managerial experience than Martinez and Sousa put together
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Adkins, 45, has emerged as a leading contender too and it is understood that there is also mileage to him being linked with the club.
The last three managers - Kenny Jackett, Roberto Martinez and Sousa - have all been rookie appointments and it is unclear whether they may go with the same again or opt for experience.
Brighton boss Gus Poyet fits the rookie bill, but distanced himself saying he was about to sign a new four-year deal at the Withdean.
Former Middlesbrough manager Gareth Southgate appears to have ruled himself out, likewise Tony Mowbray who has been out of work since being sacked by Scottish giants Celtic in March.
Swansea-born John Hartson is said to interested applying for his first managerial job while seasoned boss Chris Coleman has been touted despite previously stating he could not manage his hometown club.
Also in the frame is Sheffield United coach Gary Speed, the former Wales captain, who was a consideration last year to replace Martinez before Swansea opted for Sousa.
Wales manager John Toshack this week told the BBC that the Liberty Stadium hot seat could be an ideal first managerial job for Speed, 40, who won 85 caps for his country.
Pre-season training is being taken by coaches Alan Curtis and Colin Pascoe until Sousa's successor is found.
Source: BBC Sport
Source: BBC Sport