Manchester United's pursuit of a late second goal against Arsenal was a good reflection of their attempt to appoint a director of football. You just knew they weren't going to get it.

Under Ole Gunnar Solskjaer, United have scored twice or more in just one of their past 15 matches in all competitions, a stat that grows more worrying with every passing minute.

Against Arsenal, the image of Solskjaer berating Andreas Pereira for not sticking to the right flank was a fitting one for his time in charge. Trying to force a limited central midfielder to play as a winger seemed less a square peg in a round hole and more a two-by-four thrust into a dental cavity - and no less painful to experience.

Axel Tuanzebe as de facto left-back was not much better, nor was the persistence with Jesse Lingard as the roving number 10, a man whose Premier League goals and assists columns for 2019 show zero and whose confidence level is even lower.

It's starting to look like Solskjaer, too, is the wrong choice for United manager. The solution? Make him the new Head of Football instead.

For the past year, United have allegedly been drawing up a list of candidates for the director-of-football-type-role and still got nowhere near actually hiring someone. The names linked have ranged from people experienced in the line of work, like Norwich City's Stuart Webber and Paul Mitchell of RB Leipzig, to those with a stronger affinity for United and the brand, such as assistant manager Mike Phelan and former stars Rio Ferdinand and Darren Fletcher.

Still, in a conference call with investors last week – money is still not a concern, as record revenues show – executive vice-chairman Ed Woodward hinted at some progress: the job at least has a name.

"Regarding the speculation around the Head of Football, we are continually reviewing and looking at the potential to evolve our structure on the football side," he said. "Much of the speculation around this type of role revolves around recruitment - an area that we've evolved in recent years.

"As we've already mentioned, we feel the players we've signed in the summer demonstrate this approach is the right one."

So, no nearer an appointment. But, as Woodward intimated, the right man is already at Old Trafford. He's just in the wrong job.

United's three major signings of the window - Harry Maguire, Aaron Wan-Bissaka and Daniel James - were prudent bits of business that improved the squad and pointed to a longer-term vision for recruitment. United have not been able to say all that in the same breath since Alex Ferguson left six years ago.

While the transfer talks were handled by Matt Judge, United's chief negotiator, these were Solskjaer's signings, recommended by Solskjaer, to be implemented into Solskjaer's reconstruction of the first team. Discussions about January incomings are already underway, but nobody will join unless they fit Solskjaer's ethos of what constitutes a Manchester United player.

Solskjaer, in this way, is shaping United transfer policy with greater guile than David Moyes, Louis van Gaal or Jose Mourinho. Crucially, Woodward is buying into it. The onus is not on quick-fixes or names who carry obvious commercial appeal but on bringing in players to fit a footballing policy and removing those who don't. Solskjaer deserves credit for that. It's what a good director of football does.

Beyond the transfers, Solskjaer is relaying the path from youth ranks to first team. In July, his old team-mate Nicky Butt was moved into a new role, Head of First Team Development, to work specifically with the manager in identifying youngsters ready for first-team exposure and facilitating their move into the senior picture. The academy itself is now run by Nick Cox, formerly of Sheffield United and, interestingly, a graduate of Manchester Metropolitan University's Master of Sport Directorship course.

This reshaping of the academy, which started before Solskjaer's appointment as permanent manager but has been accelerated since, is bearing fruit in Mason Greenwood, Tahith Chong, Angel Gomes, Brandon Williams, James Garner and Tuanzebe, all of whom are in the squad for Thursday's Europa League trip to AZ. Will they radically change United's fortunes this year? Probably not. But they are United boys, they fit the Solskjaer ethos, and they deserve their chance to try.

Games like the Arsenal draw highlight Solskjaer's managerial shortcomings. He does not look like an elite-level coach who can coax the best from the talent at his disposal or produce tactical masterplans to flummox the finest opposition (which Arsenal are not). United should already be looking to hire someone who can do those things while letting Solskjaer continue the development of the club framework from a position upstairs.

Solskjaer 'gets' United: their history, their expectations, the demand for style and substance and the players needed to fulfil those requirements. He gets the importance of the academy and how to build bridges to the first team. He gets the importance of singlemindedness in the transfer window and has shown he can deliver the right signings. He should get the Head of Football job.