But there could be a twist because Liverpool are testing the water with James Milner, and it is thought Rfa Benitez will push forward a bid this week.
Emre left Turkey's European Championships training camp at the weekend to discuss personal terms with Fenerbahce after Newcastle accepted an offer of around £4m.
Riise For Milner? Could It Happen?
According to the Chronicle, that money has already been earmarked for a formal offer for Riise.
The Norwegian has been deemed surplus to requirements at Anfield, and Newcastle are also ready to make a move.
Keegan has prioritised the purchase of a left-back this summer and current first-choice, Jose Enrique, could be on his way back to Spain.
27-year-old Riise, according to reports from Merseyside, is considering Newcastle's interest.