Roberto Martinez watched the Scottish Premiership club's clash with Hibernian on Sunday and the Merseyside club are reportedly set to offer £750,000 for the teenage left-back.
The Tannadice club are understood to want £1.5 million for a player they only signed from Queen's Park in June.
United boss McNamara has revealed the club have not received any bids for the 19-year-old and thinks it would be in his best interests to stay put for the time being.
"It's a compliment if anything if someone like Roberto Martinez comes to watch some of our young players," McNamara told Sky Sports News. "There is a lot of speculation at the moment, which we are just having to get used to.
"We have had no bids for any of our players. We have had a couple of phone calls and some enquiries but that's as far as it has gone.
"Andrew just joined us last summer. He is only 19 and has just had six months with us. I think how he's done since he has joined us has been fantastic.
"I genuinely think the best thing would be for him to stay with us at least until the summer and continue to learn and enjoy his football.
"I speak to all the young lads about the speculation and when a bid comes in I will inform them of that."
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