Brian O'Driscoll: Ulster a 'basket case' at the moment
Brian O'Driscoll has described Ulster as a "bit of a basket case" in response to the issues facing the province.
The former Ireland captain said players could be reluctant to move to Belfast if they are not challenging for titles.
They are struggling to reach the Pro14 play-offs and need a new head coach.
Jackson and Stuart Olding were both cleared of rape last month after a nine-week trial but their contracts were terminated following an internal review by Ulster and the IRFU.
There had been controversy over social media during the court case in relation to WhatsApp messages involving the pair.
Senior players Tommy Bowe and Paul Marshall will retire this summer and full-back Charles Piutau will leave to join Bristol, which has left the club facing a difficult rebuilding process.
Ireland head coach Joe Schmidt and IRFU performance director David Nucifora want either Carbery or Byrne to play at the Kingspan Stadium next season, with Leinster flanker Jordi Murphy having already agreed to make a similar switch.
"Potentially one of those, Carbery or Byrne, could leave a winning culture, a winning environment," O'Driscoll told Off The Ball AM on Newstalk radio.
"You look at someone like Jordi Murphy. I have to say, it can't be easy playing some of the best rugby of his life - both from a Leinster perspective but also from Jordi's perspective - where things are clearly not going right at Ulster.
"They don't have a coach, [they're] a little bit of a basket case at the moment, and he's going up there to try and play his rugby from next year on."
O'Driscoll later defended his analysis of Ulster's disappointing season on social media and said it would take up to five years to rebuild the team.
"Well that's how it looks from the outside," he said on Twitter.
"Administration issues, senior players retiring, the well documented court case, now no number 10 to build the team around, no coach next year, struggling for Champions Cup rugby next season."
A bonus-point win against Glasgow Warriors in their final home game of the regular Pro14 season has set up a possible European play-off against Ospreys but Ulster could still secure automatic qualification for the Champions Cup if they can overtake Edinburgh in the Conference B table.