Lampard was handed his first managerial job at Pride Park in May and the 40-year-old has been tasked with getting Derby back into the top flight.
The picture looked all the more rosy for Lampard as Derby made the perfect start to life in the Sky Bet Championship last weekend with a late win at Reading.
However, that all came crashing down on Saturday when Lampard's first competitive match at Pride Park ended in a chastening 4-1 defeat to Leeds.
Shortly after Leeds' penultimate goal of the game, Lineker, who worked with Lampard at both BT Sport and the BBC, tweeted the former Chelsea star offering him his job back as a pundit.
Lampard made numerous appearances as a pundit last year - impressing during his appearances on BT Sport's coverage of the Champions League and FA Cup and at the World Cup with the BBC.