With Martinez looking on from the Anfield stands in preparation for the game at Goodison Park next Tuesday, Rodgers' team were second best in the first half on Saturday against Aston Villa.
Trailing 2-0 to goals from Andreas Weimann and Christian Benteke, the visitors threatened a repeat of their shock victory last season.
Liverpool fought back, however, as Daniel Sturridge scored just prior to half-time, whilst Steven Gerrard struck a penalty early into the second period to earn a point.
Despite the lacklustre showing, ahead of the next league clash with their local rivals, Rodgers said: "He will know how I work and knows how my teams work
"But he will know it will be a totally different game here for the derby.
"It wasn't one of our better days (against Villa), but we've had many great games here."
Speaking to the Daily Post, Rodgers added: "We'll be ready for the derby game for sure."
Rodgers, meanwhile, is being heavily linked with a move for Basle winger Mohamed Salah.
Rodgers confirmed after Saturday's game to meeting with owner John W Henry and chairman Tom Werner, apparently receiving assurances there is money available this month to strengthen.
Salah has reportedly long been on Rodgers' radar, and whilst a bid of £8million is being suggested, Basle may demand double that figure.