The Reds have been looking for someone to take over since Jose Morais was sacked on the final day of the season following the club’s relegation to League One.
Ainsworth (inset) has impressed by leading the Chairboys to promotion from League Two on a tight budget.
Barnsley were interested in luring him away in February, after Paul Heckingbottom’s departure, but their approach was rebuked.
Chief executive Gauthier Ganaye and the board members are taking their time in appointing Morais’ successor after rushing to get the Portuguese manager in last time around.
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The club whittled the potential names down to a shortlist and are carefully deliberating over who they want to take over at Oakwell - to avoid a repeat of the Morais debacle.
It is understood the club are also interested in Paul Hurst after he failed to get Shrewsbury promoted via the play-offs. Hurst’s availability was believed to be down to whether or not he led the Shrews to promotion.
However, former Barnsley player Grant McCann is the overwhelming bookies’ favourite despite being fairly inexperienced.
McCann plays an attacking brand of football which is easy on the eye. The 38-year-old’s only taste of management was at Peterborough United, initially taking over on an interim basis before getting the job permanently.
He took Posh to a respectable mid-table finish in his first season and the club were on the verge of the play-offs before a seven-game winless run saw him axed.