"All the players are talking about what he (Mourinho) wants to win. The few games we've had so far you can see the fear factor returning and that's what Manchester United is all about," said the forward who made 275 appearances for United from 1995 to 2001, before joining City late in his career.
"These past few years teams have gone to Old Trafford believing they can win. When you played under Sir Alex Ferguson teams would just hope they wouldn't get beat by five.
"Mourinho is bringing that back now and they're starting to look like the old United," Cole said in a column for online bookmaker 888.
United, who finished last season in fifth place, won the last of their record 20 English league titles in 2013.
The former England front man likened Mourinho to the manager who bought him in 1995 for a then-British record seven million pounds.
"Jose has the same great aura about him as Sir Alex. Look at what he's done in the game – going to Italy and Spain and doing it out there - and now he's trying to emulate his phenomenal record in England."
After a modest playing career, Portuguese Mourinho has enjoyed something of a Midas touch as coach. He won six trophies at Porto including the UEFA Cup and the Champions League; seven at Chelsea; five at Inter Milan including a second Champions League trophy; and three at Real Madrid.
Expectation at Old Trafford is sky-high, but Cole said it was impossible to call who would have the upper hand this season.
"If I knew who would do best in the next three years then I'd head straight to the bookmakers," he said.
After three games of the season, City, Chelsea and United all boast a 100 percent record, with City top on goal difference.
Something will have to give on Saturday when United welcome neighbours City to Old Trafford, while Chelsea visit Swansea City on Sunday.
(Editing by: Amlan Chakraborty)
