United sacked Ruben Amorim on Monday morning following his comments against the board after the draw with Leeds United last weekend.
Darren Fletcher has since taken over as interim manager, whilst Ole Gunnar Solskjær and Michael Carrick have been tipped as potential caretaker managers until the end of the season.
A new permanent manager will be decided at the end of the season and speaking on the Rest is Football podcast, Lineker asked whether the Red Devils can still attract a top manager.
Micah Richards said: “I still think they’ll want the job. As a manager, you’ll always think you can turn it round.
"I think the key question will be, ‘Do you have full control? Are you a coach, or are you a manager? Do you get to pick the players that you want? Are you having people above you meddling with what you want to do on the pitch?'
"If you have full control, 100 per cent.”
Solskjaer had a near three-year spell as the club's head coach before being given his marching orders. Currently, the Norwegian is the favourite to take the job but is not considered a world-class manager.
Newcastle United boss Eddie Howe and Crystal Palace manager Oliver Glasner have also been linked with the role as the United board decide their next steps.