The 26-year-old, who left United in 2012 for the Foxes in a £1million, has been linked with a return to Old Trafford.
It is claimed manager Jose Mourinho has identified him as a January target despite the England international recently signing a new £90,000-a-week five-year contract at the King Power Stadium.
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Leicester want a swap deal with Man United for Morgan Schneiderlin in any deal for Danny Drinkwater
But the Sunday People claim if any deal was to be struck between the two clubs then Ranieri would like to recruit Schneiderlin in exchange.
The France international has failed to live up to the £25m price tag that saw him join the club from Southampton last summer.
And he could be used as bait by Mourinho to secure a deal for £20m-rated Drinkwater.
Schneiderlin, 26, failed to make the squad for Saturday's 4-1 win over the defending champions after playing in the EFL Cup victory at League One side Northampton.
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