"I would like to say we are a little bit further down the line than we were a couple of days ago," said Jenkins.
"I just hope we get everything sorted and I would like to think so by the weekend."
Jenkins has all but admitted defeat in the chase for former Wales captain Gary Speed after Sheffield United, where he is on the coaching staff, turned down two approaches.
And he also says he expects Hamilton boss Billy Reid's refusal to have talks to be the end of that matter.
"We are still pursuing a couple of options," added Jenkins.
"They are the same options that we've been looking at for the last week just going through the fine detail making sure we find the right man to continue what we've started at Swansea City and get us ready for the start of the new season."
"It's taken a bit longer... but I think we are getting there slowly."
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Swansea parted company with Sousa last week after one year in charge when the two-times Champions League winner decided he wanted to talk to Leicester, where he was eventually appointed.
Jenkins had hoped to make a swift appointment, initially saying he wanted a new manager in by Monday, which came and went without success.
He has previously named Rochdale's Keith Hill, Eddie Howe at Bournemouth, Bristol Rovers boss Paul Trollope and Terry Skiverton of Yeovil Town as the type of young British manager he is looking for.
Other names to have been linked to the post include ex-West Ham boss Gianfranco Zola and his assistant Steve Clarke along with Wigan assistant manager Graeme Jones.
Exeter's Paul Tisdale and Brighton's Gus Poyet have distanced themselves from the job, while Bournemouth have warned against an approach for Howe.
Source: BBC Sport
Source: BBC Sport