Rodgers is a good manager, his record speaks for itself.
But I don't think he's equipped to handle top teams which naturally populated by top players.
The story of how handled his time at Liverpool is discouraging, on how he couldn't confront his own players.
If United were to employ him, sure he could probably get them to compete for top 3 but provided he has some raw materials to work with.
The current crops over at Leicester are decent: Vardy is reliable albeit waning, Maddison, Chilwell, Ricardo, Tielemans, Ndidi, Schemeicel and Gray are all good/promising players.
United's current squad contains DDG, Pogba, Rashford, Maguire, AWB and the much maligned Fred.
His record of signing players are sketchy though, United should not trust him to magically counteract Ed Woodward and make everything right.