Gerrard has already brought six new players to Rangers since his arrival at Ibrox as many weeks ago.
Steven Gerrard hopes to persuade Jordan Jones join Rangers ahead of Frank Lampard's Derby County, according to the Daily Mirror (June 17th, page 68).
Jones has long been linked with a move to Ibrox and Rangers' interest does not appear to have waned despite Gerrard's appointment in May.
However, the former England captain is said to face competition for the Kilmarnock winger's signature from a string of clubs - with Derby, Hull City and Preston North End all named in the Daily Mirror's report.
Rangers have signed six players in as many weeks since Gerrard's arrival, with wide man Jamie Murphy among them.
However, the Ibrox side continue to be tipped to strengthen in Jones' position, where Liverpool pair Ryan Kent and Harry Wilson have been prominently linked.
And with Jones priced in the region of £600,000, according to the Daily Mail, the Northern Ireland international could be Rangers' most attractive option.
Gerrard and Lampard were teammates for England and later worked together as BT Sport pundits before landing their first managerial jobs, at Rangers and Derby respectively, this summer.
Would Rangers be a better move for Jones than Derby, Hull or Preston?