England U18 defender Mengi completed a deadline-day move to Derby, joining the Championship side on loan until the end of the season.
Mengi is one of the most highly-rated young players at Old Trafford and made his senior debut last August in United’s Europa League victory over LASK.
The 18-year-old will hope to establish himself as a first-team regular at Derby and Solskjaer wants him to impress manager Rooney, who is Manchester United’s all-time record goalscorer.
‘When you get to his age, sometimes there aren’t enough challenges in every game,’ Solskjaer said of Mengi.
‘It doesn’t prepare him enough for that physical striker or forward that he might meet in the first team.
‘So to play in the Championship is a great challenge for him.’
On Mengi linking up with former Manchester United and England captain Rooney, Solskjaer added: ‘Yeah, that’s going to be good for him.
‘Wayne’s been a top striker. I’m sure he’ll go in there and show him a few things himself.’
After signing with Derby, Mengi said: ‘I’m really excited and buzzing to be here.
‘When I heard Derby were interested I thought it was no-brainer for me. I’m really happy to be here and to be playing in the Championship.’
Manchester United also sent Facundo Pellstri out on loan on deadline day, with the Uruguayan winger joining Alaves.
Solskjaer said: ‘Yeah, we feel that he has taken some good strides when he’s been here and we looked at a few options, but that was a good option.
‘He felt comfortable and confident going there, so hopefully he’ll get some important matches in a good league.’
For more stories like this, check our sport page.