The Red Devils were the closest challengers to record-breaking rivals Manchester City in 2017-18, but still finished some 19 points off the pace.
Only minor tweaks have been made to the playing staff at Old Trafford since then, with Brazil international Fred representing United’s most notable piece of business.
Mourinho remains in the market ahead of the window slamming shut on Thursday, and Rooney hopes to see late movement that will make his former club more competitive.
United’s all-time leading goalscorer told Sky Sports: “I think it will be difficult after the season they had last year. They [Manchester City] have been playing some great football.
“But I hope someone can catch them - it would be nice, so hopefully Manchester United can. I think maybe another signing or two.”
Mourinho has been left frustrated in his efforts to get further deals over the line, sparking reports of a breakdown in his relationship with executive vice-chairman Ed Woodward.
Those issues have provided an unwelcome backdrop to a difficult pre-season, United’s makeshift side having suffered defeats to Liverpool and Bayern Munich.
They are now a little over 24 hours away from opening the new Premier League campaign, with Rooney looking for the Red Devils to put any problems behind them and lay down an early marker in the battle for top-flight supremacy in England.
“I know there has been a lot of talk about pre-season in the press but I am sure behind the scenes, Jose has been giving them the right amount of work.
“They have the game against Leicester on Friday so hopefully they can go one step further this year than second and try and get the title back.”