Solskjaer replaced the sacked Jose Mourinho as Manchester United interim boss in December.
The Norwegian had a stunning start in the role, winning his first nine away games in all competitions.
Solskjaer has led United into the quarter-finals of the Champions League after a stunning comeback win over Paris Saint-Germain in the last 16.
United have lost their last two games though, against Arsenal and Wolves in the FA Cup, leading to potential doubts over Solskjaer’s suitability in the role.
But Townsend still believes Ole Gunnar Solskjaer is the right man and believes the club are waiting for the lead up to the big upcoming matches against Barcelona or rivals Manchester City to make an announcement.
“I’ve actually spoken to Mike Phelan [United assistant manager] a few times since they’ve been in charge,” Townsend said on BBC Radio 5 Live.
“Micky said: ‘It’s not been rocket science what we’ve done here, it’s actually been quite straightforward but we’ve been determined about the way to go about it’.
“But it’s not reinventing anything here or coming up with anything unbelievable.
“It’s reminding players how good they are, where they are, and then drilling it into them morning, noon and night and then putting demands on them but backing them and trusting them.
“I don’t think anyone [could have done a better job].
“Are they waiting for the perfect moment now for them to say ‘it’s yours’.
“Is it before the Champions League game or is it before the City game coming up?
“Is it before one of those where they actually announce it and it’s like ’boom’ all of a sudden it takes off again just before a big game? Probably, probably, rather than waiting until the summer.
“He’s done more than enough to warrant being given that job now.
“United have been able to give him the perfect audition, they’ve given him plenty of games, they’ve seen what he’s done.
“He’s come through some tough games, some really awkward ones, and has, in the main, been a roaring success.”
United host Barcelona on April 10 in their Champions League quarter-final first leg and play City at Old Trafford in the Premier League on April 24.