Rush has suggested Rodgers' Liverpool history could be a factor in any decision he has to make over the United job.
"I see the top football betting sites are offering short odds on Brendan Rodgers being the next manager of Manchester United, but all indications are that he's happy at Leicester and he's building something really strong there," Rush told Gambling.com.
"It might be that the job is too big for Rodgers to turn down – United are a huge club – but having already been Liverpool manager I think he'll know the scale of the rivalry between the two clubs and that could play a factor in any decision if he gets offered the job.
"He appears happy where he is though so it'll be interesting to see what happens if United do come calling."
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