The inaugural 100-ball competition, which is comprised of eight city franchises, takes place next summer from 17 July-16 August.
Other big names to have stated their interest include Afghanistan spinner Rashid Khan, australia opener David Warner and former Pakistan all-rounder Shahid Afridi.
England’s contracted Test players such as Joe Root, Ben Stokes and Jofra Archer are not on the list because they will be part of an initial draft for England’s red-ball cricketers on Thursday.
In that mini draft, teams will select up to three players, with the Leeds-based side, for instance, having to choose between Root, Stokes and Jonny Bairstow as their first pick.
They will also have the opportunity to select local icons. The eight teams will be based in London (two teams), Birmingham, Manchester, Leeds, Nottingham, Cardiff and southampton.
The main draft will be held later this month and among the other international cricketers to have made themselves available for the competition are Shakib Al Hasan, Moeen Ali, Babar Azam, Tom Curran, Quinton de Kock, Faf du Plessis, aaron finch, Lasith Malinga, Kieron Pollard, Kagiso Rabada, Jason Roy, Mitchell Starc and Kane Williamson.
Players are able to set a reserve price for their services, with each team having two spaces in their squad in each of the following pay brackets: £125,000, £100,000, £75,000, £60,000, £50,000, £40,000 and £30,000.
England limited-overs captain Morgan is a vocal supporter of the new competition, which will see live cricket return to the BBC.
Speaking earlier in the summer, Morgan said: “The Hundred, yes, I do think we need it. We need one franchise-based tournament, with fewer teams, in order to consistently sell the game to the country.
“Anybody I speak to who loves sport but doesn’t necessarily love cricket is crying out for a tournament that he or she understands, because 18 teams going for a long period of time just doesn’t make sense to anybody.”