The return of the inspirational No 8 will sow a few doubts in the Ireland camp ahead of Sunday's game in which they could secure a quarter final place from Pool D.
The 32-year-old underwent an operation the week before the World Cup began to drain a haematoma on an injured right calf.
A specialist in Paris cleared him on Monday to join the squad, the Italian rugby federation said.
"Parisse will continue therapy at the training camp in England and later in the week will be evaluated to see if he is ready fo the test of the World Cup match against Ireland on Sunday," said a statement.
Parisse is the one player who can turn the Italians from the sloppy unit they appeared in a heavy loss to France and a narrow victory over Canada into a team ready to challenge Ireland, the Six Nations champions' skipper Paul O'Connell said.
"Parisse makes a massive difference for them, he's obviously a world-class player," said O'Connell.
The Irish have looked in impressive form in Pool D, dispensing easily of Canada, 50-5. Then a revamped XV coasted to a 44-10 victory over Romania.
Now, though, they face their toughest two encounters against Italy and a top of the table showdown with France. A win over the Italians at the Olympic Stadium on Sunday would see them qualify for the last eight.
Parisse will undoubtedly have an impact if he plays, according to O'Connell.
"A lot of their defensive and attacking lineouts run around him, we talked about having 100 per cent set-piece (against Romania) - it's going to be a lot harder to do that against Italy.
"Around the field he can produce that something different, that maybe the teams in the last two weeks haven't had. So we've got to be ready for that," added O'Connell.
O'Connell's second row partner Devin Toner also said Parisse had the ability to transform the Italian side.
"Parisse would definitely change the dynamic," said Toner, who stands at a whopping 2.08m (6ft 8in).
"He controls the lineout, he owns it, he calls it: so he's a real threat if he does play.
"But he's the talisman, he spurs everything good about Italy. So if he does play it would be a coup for them. You never want to see players injured of course."
"I'm sure the neutrals want to see him play but I don't know if we do to be honest!" added the 29-year-old.