Described in his club profile as "fast, direct, and above all a fine opportunist in front of goal", Graver soon attracted attention from other clubs. Early on in his Lincoln career the club rejected an offer of £12,500 from Norwich City for his services. Nottingham Forest made several bids for the player. In December 1954, he signed for First Division strugglers Leicester City for a fee of £27,500 plus the player Eric Littler, valued at £600, a Leicester City club record, and little below the £30,000 paid by Tottenham Hotspur for Northern Ireland international and Aston Villa captain Danny Blanchflower not long before. Graver, described as "reluctantly" leaving Lincoln, said he was "afraid of the responsibility of living up to such a price tag".
