The 29-year-old Cunningham, who has 128 Ulster caps to his name, is in direct competition with Australian Mark Bartholomeusz for the number 15 jersey.
Also included in the extended squad are Academy player Mark McCrea, hooker Matt Miles and Justin Harrison who played for the Barbarians against South Africa last Saturday.
Commenting on Friday's game, Steve Williams said: "Again, like everything else we have to pick the team for the different oppositions and the challenges that they will present. We need to be streetwise against the Ospreys and we are well aware of the threats that they bring to the game."
Ulster currently have three back row players unavailable due to injury with Roger Wilson joining the list, alongside Stephen Ferris and Neil McMillan, after sustaining a thumb injury against Edinburgh. The injury is likely to keep Wilson sidelined for between six and eight weeks.
Out-half David Humphreys is also still unavailable due to the ankle injury which has troubled him since pre-season.
Williams, who will name his team and replacements on Thursday, added: "The Ospreys have a stellar squad with fantastic players and it will be interesting to play against a team of their calibre."
ULSTER Squad (v Ospreys): Backs (12) - Mark Bartholomeusz, Simon Danielli, Bryn Cunningham, Mark McCrea, Tommy Bowe, Andrew Trimble, Rob Dewey, Paul Steinmetz, Niall O'Connor, Paddy Wallace, Isaac Boss, Kieran Campbell.
Forwards (13) - Justin Fitzpatrick, Bryan Young, Declan Fitzpatrick, Matt Miles, Rory Best (capt), Nigel Brady, Justin Harrison, Ryan Caldwell, Carlo Del Fava, Matt McCullough, Neil Best, Kieron Dawson, David Pollock.