Jones was part of the Blackburn team who drew 1-1 with United last May which ensured Sir Alex's men were crowned champions.
The defender is hoping for a repeat scenario this season and three points at Ewood on Monday night would be another important step towards that.
[The scenes at Blackburn last season] are exactly why I left," he told ManUtd.com.
"I have fond memories from my time at Blackburn and there are some wonderful people at the club. But I wanted to win trophies and become part of a team with a massive history, which United have.
"To lift that trophy at the end of the season would be a wonderful achievement for me.
"No game is easy in the Premier League," he added. "The teams we have got coming up are scrapping for their lives. They will all be difficult games.
"It is nice to be top but we can't keep looking at the table because we have a long way to go before we are anywhere near to picking up that trophy. Hopefully we will get the three points on Monday night."
Jones says he spoke to a few of his old team-mates at Rovers earlier this month ahead of next week's clash and while they still remain dangerously close to the dropzone, he is pleased to see they have turned things around and given themselves a chance of survival.
"They had a really tricky start to the season and Steve Kean got a lot of stick and came under a lot of pressure," recalls Jones. "He deserves a lot of credit - you don't hear a lot about Blackburn or