Newcastle's director of football Joe Kinnear wanted the former England striker as his assistant.
But Harford, who spent a short time at St James' Park as a player in the early 1980s and worked with Kinnear at Wimbledon, has declined the offer.
The 54-year-old last month joined the coaching staff at Millwall, and he told Sky Sports News: "After meeting with Mike Ashley and Joe Kinnear, I made the hard decision that it is not the right time for me to take up this role.
"It was an honour to be asked to work at a fantastic club and I have the utmost respect for the Newcastle United and its fans.
"I am currently enjoying a role helping out at Millwall, but would like to thank Mike Ashley and Joe Kinnear for the opportunity."
RIO AVE 3 NEWCASTLE UTD 1
RIO AVE: Ederson, Tarantini, Hassan, Diego, Braga, Vilas Boas, Dias, Marcelo, Lionn, Del Valle, Wakaso.
NEWCASTLE UNITED: Alnwick (Elliot, 46); Santon (Williamson, 70), S Taylor, Yanga-Mbiwa, Dummett; Cabaye (Tiote, 46), Anita (Campbell, 76); Marveaux (Obertan, 46), Vuckic (Sissoko, 46), Gutierrez (Sammy Ameobi, 46); Gouffran (Shola Ameobi, 62).
Alan Pardew's men travelled to Portugal without star striker Papiss Cisse, who was left behind amid a disagreement with the club over his refusal to wear kit sponsored by loan company Wonga.
And Newcastle's lack of firepower proved telling as Rio Ave seized the initiative to seal a comfortable win.
Pardew plumped for a mix of youth and experience in his starting XI, with inexperienced goalkeeper Jak Alnwick and full-back Paul Dummett named alongside the likes of Yohan Cabaye, Steven Taylor and Jonas Gutierrez.
This game probably gave Pardew more questions than answers, and it will be a 45 minutes that Jak Alnwick will not forget.
Managers always play down the importance of such games, saying the result doesn't matter, the performance does ... but if Pardew is looking for positions he needs to strengthen ... he could include goalkeeper.
Tim Krul is still fighting to recover from the injury he picked up against the Mackems months ago, and Rob Elliott is not a player I'd put in the same class as others who have worn the goalkeeper's shirt - he ain't no Pavel or Shay.
Do we need cover there? You tell me!
United started slowly, and quickly found themselves two goals behind, with Egyptian striker Ahmed Hassan netting a quick-fire double in the first nine minutes.
Newcastle's worries only increased, and after 26 minutes they were 3-0 behind as midfielder Braga scrambled home from close range.
The visitors did improve somewhat as the half wore on, and will have felt unlucky not to have cut the deficit as a Cabaye effort rattled the crossbar four minutes before the break shortly after Ederson had produced a fine diving save to deny Sylvain Marveaux.
Pardew made five changes during the interval, with Rob Elliott, Sammy Ameobi, Moussa Sissoko, Gabriel Obertan and Cheick Tiote all introduced into the action.
The alterations had an impact, with Yoan Gouffran shooting wide after good work down the right from Obertan after 57 minutes.
It was Gouffran's eventual replacement that would haul Newcastle back into the game however, as Shola Ameobi steered in Obertan's right-wing cross to reduce the arrears with 14 minutes to play.
The game ended sourly for the striker, though, as he was taken to hospital afterwards for x-rays on an arm injury, which forced him off.
Newcastle could not complete the comeback, though, and it was the hosts who wasted a chance to have the final say, substitute Sandro Lima seeing his penalty saved by Rob Elliot four minutes from the end after he had been bundled over by Mike Williamson.
WE TELL IT AS IT IS - NO BULLSHIT!
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RIO AVE 3 NEWCASTLE 1 (Shola Ameobi)
Alnwick (Elliot, 46); Santon (Williamson, 70), S Taylor, Yanga-Mbiwa, Dummett; Cabaye (Tiote, 46), Anita (Campbell, 76); Marveaux (Obertan, 46), Vuckic (Sissoko, 46), Gutierrez (Sammy Ameobi, 46); Gouffran (Shola Ameobi, 62).
MOTHERWELL 2 NEWCASTLE 4 (Vuckic, Gouffran, Sissoko, Marveaux)
Elliot; Tavernier, Williamson (S Taylor, 46), Yanga-Mbiwa (Streete, 82), Dummett; Sissoko (Abeid, 68), Anita (Amalfitano, 82); Obertan (Ferguson, 74), Vuckic (Marveaux, 46), Sammy Ameobi (Richardson, 82), Gouffran (Campbell, 58).
Sub not used: Alnwick.