And with Rooney linked with moves away from the club, with little game time this season, Keane thinks this could the record scorer's a year ago at Old Trafford.
Burnley rarely looked likely to make a comeback and United were able to conserve energy in the second half after their exertions against Anderlecht in the Europa League, though they may have another injury concern to contend with after Paul Pogba limped off late on.
Burnley won their first ever home Premier League match which was against Manchester United in August 2009.
While clubs are looking at Keane - Everton manager Ronald Koeman publicly expressed his interest back in January - Dyche stressed it is far from a foregone conclusion that he has the final stretch of his Burnley career under him.
The no-nonsense midfielder heads into Sunday's Premier League clash at Burnley having already made more appearances for the club this season, 41 in all competitions, than in any campaign since his £27.5 million from Everton in 2013.
"They're not short of options, without a shadow of a doubt", Dyche told reporters.
"You get to an age where you're questioned regardless of performances. Whatever his journey forward is he will remain a top-class player in my eyes".
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Manchester United have scored just once in their last four league games at Turf Moor, with that goal coming from Lou Macari in April 1976. "We had to give every bit of air in our lungs to try and get something".
Furthermore, they could score three times in an away match for a fourth league game in succession for the first time in 17 years, having brushed aside Sunderland, Middlesbrough and Leicester City in recent weeks, conceding just once in the process.
Mourinho said: "We're in trouble". A source, apparently. I'm always a good source, as manager. We're certainly not under any consideration of our players leaving at this moment in time.
With Rooney now seemingly little more than a squad player, United legend Keane expects him to move on at the end of the season.
We all know about Burnley's home record, and this is a tough one for Manchester United straight after their Europa League tie against Anderlecht.
"He is a strong man, even if he is not in the best condition, even if he is not in the level of sharpness that you need to play high-level football, but he has the experience and character, so he has to".