The former Spurs man says ex-United boss Sir Alex Ferguson wanted to sign him after he had scored for England against Sweden in 1995, with Red Devils defender Gary Pallister helping to broker the move.
Ferguson had reportedly heard that Anderton had a release clause in his contract - which Lord Sugar was determined to remove.
Anderton told the 'Quickly Kevin, Will He Score?' podcast: "That was when United came in, after that game.
"Pally - Gary Pallister - went, 'Do you fancy coming to play for us?' as we were all having a game of snooker back at the hotel.
"He just said, 'Can I give the gaffer your number?'
"'Yeah, why not?'
"It was a little bit daunting to be fair. Though it was more daunting for my brother, who answered the phone.
"The next day I went and saw the chairman Sir Alan Sugar and he didn't let me leave his house without signing a new contract to get rid of that clause.
"It was a bit panic stations because Jurgen Klinsmann had said he wasn't going to stay, Gheorghe Popescu was going to Barcelona and Nicky Barmby wanted to leave."
Anderton never made that move to United and missed out on winning numerous league titles under Ferguson. Gutted.
Barcelona 
Osasuna 
Krylya Sovetov 
Lokomotiv Moscow 
Aubagne 
Bordeaux 
Bayer Leverkusen 
VFL Bochum 
Strasbourg 
Lyon 
Gil Vicente 
Benfica 
Obolon-Brovar Kyiv 
Shakhtar Donetsk 
Sampdoria 
Frosinone 
Bayern Munich 
FC ST. Pauli 
Holstein Kiel 
Werder Bremen 
VFL Wolfsburg 
FC Heidenheim 
Celtic 
Heart Of Midlothian 
Espanyol 
Atletico Madrid 
Reims 
Marseille 
Rukh Lviv 
Dynamo Kyiv 
CSKA Moscow 
FK Makhachkala 
Juventus 
Genoa 
Eintracht Frankfurt 
VFB Stuttgart 
Dundee 
Rangers 
ST Etienne 
Paris Saint Germain 
Metz 
Lecce 
Roma 
Real Madrid 
Leganes 
NEC Nijmegen 
AZ Alkmaar 
Monaco 
Nice 
PSV 
Ajax 
Fiorentina 
Atalanta 
Akhmat Grozny 
Spartak Moscow 
Girona 
Feyenoord 
GO Ahead Eagles