Goalkeeper Chris Kirkland, defenders Glenn Loovens and Oguchi Onyewu and midfielder Jose Semedo have all had contract extensions put to them.
The quartet remain undecided at present, though, with Wednesday still waiting on pen to be put to paper.
There is, however, a feeling within the camp that agreements will be reached soon.
Coach Lee Bullen believes all four could end up prolonging their time at Hillsborough, with compromises expected once all options have been considered.
He told The Star: “We desperately want the four to stay.
“They all had a fantastic second half to the season. I’m remaining very positive and we are keeping our fingers crossed.
“They want to stay but it’s a short career and people are wanting to get the best deals that they can.
“Negotiations are ongoing. It’s a game of poker now between the agents and the club and seeing who blinks first.”