The Holland international has been the subject of talks involving RBL and Chelsea for several weeks.
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Chelsea have been attempting to reach terms with RBL for the midfielder, with several players offered in exchange.
However with no deal struck, talkSPORT says City are now making their interest known.
City are interested with James McAtee eager to move to Nottingham Forest and Tottenham pushing to prise Savinho away.
For the moment, City have registered their interest, though no offer has been tabled.