The Reds take on standings leader Blackburn on Sunday in a game that will have a major impact on who wins this season's Premier League title.
Rovers have a five-point lead over United, the team that edged them out for the title last season. Now Cole, signed from Newcastle for ?7 million ($11.2 million), has the chance to make an instant impact with the team and the Old Trafford fans.
A United victory would cut Rovers' lead to two points, even though Blackburn has the advantage of having played one game fewer.
A Blackburn victory at Old Trafford would put Rovers eight points ahead and that could be stretched to 11 with the game in hand. That is a big lead at this stage of the season, and the effect could be more psychological than mathematical.
Cole, 23, gets his chance because Mark Hughes is likely to be out of action for at least a month after gashing his knee against Newcastle last Sunday.
The newcomer should team up with talented Frenchman Eric Cantona in United's attack, hoping to break through the Premier League's meanest defense.
Liverpool, back in third place and 10 points behind Rovers, badly needs to make up for last week's disaster at home to next-to-last Ipswich.
Roy Evans' team lost 1-0 and now has a tough visit to seventh-place Wimbledon, where few visitors triumph.
Nottingham Forest, which is fourth, hopes to profit from a home game against lowly Aston Villa while Newcastle goes to mid-standings Sheffield Wednesday. Tottenham has climbed to sixth under the guidance of new manager Gerry Francis but not all his players apparently are happy about the tactics he uses.
Interviewed by Dutch TV, Romanian midfielder Giga Popescu, who used to play for PSV Eindhoven, accused Francis of making the team play too defensively. Ironically, the tactics of attack-minded previous manager Osvaldo Ardiles left the team in trouble after a series of losses.
"I should never have left Holland or PSV Eindhoven where they all play with progressive ideas compared with the defensive football I've found under Francis," Popescu said. "I feel absolutely out of place at Spurs."
On Saturday, Tottenham, which has gone 11 games unbeaten, hosts Manchester City and, on current form, should collect the three points.
Although Arsenal is defending its European Cup Winners' Cup title and has reached the quarterfinal, it has slumped to 13th, just four points above the relegation zone. On Saturday it goes to another struggler, Coventry.
Last place Leicester, which looks almost certain to go down, hosts mid-standings Leeds. Next-to-last Ipswich hopes to take advantage of Chelsea's erratic form while two more strugglers, Everton and Crystal Palace, meet at Goodison Park. Queens Park Rangers hopes to climb away from danger by beating Norwich at home and third-from-last West Ham visits Southampton.
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