Newcastle have made a second offer for the Slovenia striker in the last 24 hours.
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Manchester United are also interested in Sesko, but are yet to make a formal offer.
Meanwhile, talkSPORT says Newcastle have made a club record bid of €80m for Sesko - and want the proposal accepted by Wednesday night.
Newcastle do not want negotiations to drag on, having met RBL's original asking price for their centre-forward.
The only stumbling block, beyond Sesko's opinion, is RBL's insistence on a sell-on clause being included in the deal. However, Newcastle are insisting everything be settled by tomorrow evening, otherwise they will move on and look elsewhere.