The APL, which returns this year for its second edition after being launched in 2018, is scheduled to begin on December 27.
Player registration opened on September 1, with more than 1,000 cricketers reportedly registering, including over 500 overseas players.
Shakib, who has been unable to play regularly for Bangladesh, has continued his involvement in overseas franchise cricket and recently featured in the Lanka Premier League.
Taskin was also due to play in the LPL but withdrew to focus on Bangladesh's preparations for their Australia tour.
Nahid, meanwhile, has so far featured in the Pakistan Super League but has not played in another overseas franchise league.
With the APL scheduled after Bangladesh's South Africa tour, Taskin and Nahid could potentially be available for the competition.
The absence of the Bangladesh Premier League this year could also make obtaining their no-objection certificates less complicated.
Several international stars have also registered for the APL draft, including England's Jason Roy, Moeen Ali and James Vince, Sri Lanka's Charith Asalanka and Maheesh Theekshana, West Indies duo Fabian Allen and Alzarri Joseph, New Zealand's Colin Munro and South Africa's Matthew Breetzke.
The player draft was initially scheduled for September 27, but it has now been moved to October 24.
