Manchester United are ready to compete with football's elite in England and abroad again, according to Roy Keane.

After losing to Real Madrid in the European Super Cup against Real Madrid in August, United have won eight of their next nine games in all competitions since, sweeping teams aside with the swagger they have missed since Sir Alex Ferguson retired in 2013.

While United never finished lower than third in the Premier League era during Ferguson's reign, they have made the top four just once in the four seasons since his retirement. Jose Mourinho guided the club to two trophies in his first season at Old Trafford but Keane said the aim for 20-time champions of England should be clinching a first Premier League title in five years.

On Wednesday (27 September), United made it two wins in as many games in the Champions League, after triumphing 4-1 in Moscow against CSKA. Ireland's assistant manager said the performance suggested United were finally back among the best.

"United are back," he said on ITV's Champions League highlights show.

"They look like they will compete to win the big trophies. Over the last few years, you are thinking they might win a League Cup and the lesser trophies.

"But they are back competing and you expect them to be in the latter stages of the Champions League and winning the Premier League."

Keane, who captained United between 1997 and 2005, also heaped praise on Romelu Lukaku, after the Belgian scored twice against CSKA. This makes it three goals in two appearances in the Champions League this season.

Since his £75m (€85.3m) move from Everton in the summer, the 24-year-old has hit the ground running, scoring 10 goals in nine games in all competitions.

"He was a bargain at £75m, it was obvious he was going to score goals," Keane said.

"His record at Everton was fantastic and clearly he has gone to a bigger club and better team, who will create so many chances for him, he will get 25-30 goals a season.

"He has got off to a good start. He comes across well and seems like a decent character."

Lukaku will face his first big test of the campaign when United travel to Anfield to face Liverpool after the international break on 14 October, but Keane insisted Lukaku should be judged at the end of the campaign.

"The big test will be in the big games," he explained.

"For all top United strikers over the years, [the test] has been scoring the big goals in the big games.

"We are looking at these outstanding strikers all in great form but the time to judge them will be at the end of the season when the medals and trophies are being handed out.

"It's crunch games when one goal will be the difference."