With less than a year to run on his Saints deal, Ings has resisted attempts to secure him to new terms.
Instead, Ings is holding out for a bid from United or Man City this summer, according to talkSPORT.
Their transfer correspondent, Alex Crook, said: “If a big team comes in for him and that hasn't happened. I should stress that there hasn't been a single enquiry.
“He's got his sights set on Manchester United or Man City, I'm not sure either of those clubs are going to start banging on the door."
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