Ferguson believes Walsh can help with structural changes at the club, according to Sky Sports.
The report claims vice-chairman Woodward still favours bringing in an ex-United player into the role.
Walsh was head of recruitment at Leicester when they won the 2015/16 Premier League title.
He was credited with the signings of N'Golo Kante and Riyad Mahrez, and Ferguson thinks he could uncover similar gems for United.
Former United defender Rio Ferdinand has confirmed he has held talks with Woodward over the role.