Mallinder leads the way at 5/1 with Paddy Power and Coral, while Bath’s Mike Ford and Harlequins boss Conor O’Shea also seen as likely candidates.
Lancaster is under severe pressure after England’s failure at the World Cup.
The Red Rose have been eliminated from the tournament with one pool game, against Uruguay, to spare.
And though Lancaster has a contract that runs until 2020, his long-term future appears far from certain.
Mallinder, who took over at Saints in 2007, has had success coaching England sides before as he helped the Under-21 team earn a clean sweep in the 2006 version of the Six Nations.
He was then handed the chance to coach the Saxons, winning 15 of his 16 games in charge and taking the Churchill Cup with a victory over the New Zealand Maori at Twickenham.
Mallinder, who signed a new five-year deal at Franklin’s Gardens last summer, worked with forwards coach Dorian West in that setup and the pair have continued their formidable coaching partnership at Saints.
Together, they masterminded an Aviva Premiership and Amlin Challenge Cup double in 2014, as well as winning the LV= Cup, National League One and the EDF Energy National Trophy.
They also steered Saints to the final of the Heineken Cup in 2011, when they lost in agonising fashion to Leinster.
Northampton have not finished outside of the Premiership top four since 2009 and will be among the favourites again this season.