Bell and Anderson have both signed agreements confirming their appearance in the competition's draft, while Cook has been in talks with organisers for some time but has yet to confirm his involvement.
The inaugural PSL will feature five franchise-based teams from the provincial capitals - Lahore, Karachi, Peshawar, Quetta and Islamabad - with prize money of $1 million. The 24-match tournament is scheduled to run from February 4 to 24 in Dubai and Sharjah. Players will be allocated to teams via a draft to be held in December.
The dates of the tournament will prevent members of England's white-ball squad taking part as they will be required for the series against South Africa, but several other England-qualified players - including Luke Wright, Monty Panesar, Tim Bresnan, Jade Dernbach, Ravi Bopara and Michael Carberry - are also expected to appear in the draft.
Bell was recently dropped from England's Test squad for the tour of South Africa so currently does not have any competitive cricket until April while Anderson has not played white-ball cricket internationally since the World Cup.
Kevin Pietersen has also agreed to play, leading to the intriguing possibility that he and Cook could face each other, or even share a dressing room, at some stage during the tournament. The two have not spoken since the day in February 2014 when Pietersen was informed that he no longer featured in the England's management's plans. Pietersen subsequently portrayed Cook as a "decent" but weak man in his autobiography - he compared him to Ned Flanders, from The Simpsons - suggesting he spent the final meeting between the pair unable to look Pietersen in the eye.
While Pietersen hailed Cook's captaincy as "outstanding" during the Ashes and admitted that the decision to drop him had been largely vindicated by Ashes success, the two have yet to mend their personal relationship.