Rooney, who scored a club record 253 goals in 559 appearances for United before departing in 2017, admitted it was tough to see them languishing in the bottom half of the table.
Ten Hag has again come under huge pressure after just two wins from seven Premier League games this season and Rooney is hoping the Dutchman can quickly turn the club's fortunes around.
When asked if Ten Hag was the right man for the job, Rooney told Sky Sports: 'Well that's obviously down to the owners of the football club to look at that. I'm sure Erik Ten Hag is a fantastic manager.
'He's won trophies wherever he's been and won trophies at Manchester United as well.
Wayne Rooney (right) has backed Man United's under-fire manager Erik ten Hag (left)
'So yes, he's going through a difficult period and I think he'd probably say that himself.
'But you hope he can turn it around because too often managers lose their jobs and then it's another rebuild with a different manager.'
United have won just three of their 10 games in all competitions since finishing eighth in the top flight last season and Rooney questioned the players' performances.
'I think it's difficult and anyone would admit that Manchester United want to be challenging for titles, so to be 14th, I'm sure everyone at the club knows they need to improve on that,' said the Plymouth manager.
'I know Erik Ten Hag is doing everything he can to try and improve that. Players again, and I said this last season, need to do better than what they're doing.
'There's a big turnaround of players over the last few years. You just want to see them challenging again.'
When asked if he had any advice to offer Ten Hag or his players, Rooney added: 'It's not for me to give Erik Ten Hag advice. He's Manchester United manager and a very experienced manager as well.
'When you're going through a tough period the important thing is you knuckle down, you work hard, you try and do the basics right.
'I think they showed good spirit to pick up a point against Villa, but the fans probably want to see a bit more and hopefully they can start doing that.'