The former Bolton, Newcastle and West Ham midfielder has been out of work since being sacked by Notts County in August.
But following talks with the League One strugglers, the 36-year-old has been offered the chance to take over at Kingsmeadow.
AFC Wimbledon have been without a manager since Neal Ardley left by mutual consent 10 days ago.
Russell Slade, Shaun Derry and former player Wally Downes were among the candidates for the position.
However, Nolan is the front-runners and could be confirmed as their new boss on Thursday.
The club are in deep relegation trouble and are second bottom in League One having lost nine of their last 10 games.
Shrewsbury Town inflicted upon them their most recent defeat on Saturday.
If Nolan does indeed step into the hot seat his first game in charge will be against Rochdale.
He has endured a tough start to his managerial career, losing his job at Leyton Orient just six months into a two-and-a-half-year deal.
At Notts County he dragged the club away from the relegation places in his maiden season and followed it up with a run to the play-offs last term.
But a winless run of six games at the start of the 2018-19 campaign saw him sacked by the Magpies.
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