Sky Sports claim 39-year-old Lampard is closing in on a move to Derby, who will be looking to go one better than this season after losing in the Championship play-offs to promoted Fulham.
Rowett opted to join Stoke despite the club's relegation from the Premier League, and former England and Chelsea hero Lampard has since been linked with the vacant hotseat in a move that will be his first managerial role.
Former Rams captain Savage reacted to the news on Twitter, replying to Bookmakers William Hill who asked whether the appointment would be good for Lampard - to which he replied simply "Yes".
Sky Sports claim both Lampard and Derby are keen to get a deal done, though a number of contractual issues remain under discussion between both parties.
It is believed that Chelsea's Under-18 manager Jody Morris will join Lampard at Derby as part of his new-look coaching staff, after Lampard was interviewed twice for the vacant role at Ipswich Town.
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