With the Red Devils sat in seventh spot in the Premier League table, and after a 5-0 thrashing to Liverpool last Sunday, pressure on Ole Gunnar Solskjaer has quickly increased, with questions arising about his future at Old Trafford.
Leicester boss Rodgers was one of the men reportedly lined up as a possible replacement for the Norweigan, but he has since dismissed such links.
The Northern Irish manager said: "I don't even think about it - and that's the brutal honesty. I'm sure the supporters are probably tired of it. At Leicester, there is always a link. My focus is always here with Leicester and developing the football club on to that next level, where you're competing for European football and challenging for honours," as quoted by The Mirror.
Rodgers's Foxes currently sit ninth in the Premier League table, after consecutive fifth-placed finishes, and they recorded a 4-2 victory over Manchester United earlier in October.