Both Fifita and Tonetti will play for their respective clubs in the Ulster Bank League this weekend - Bucanneers and Lansdowne - and are expected to be available for selection as the province looks to the Heineken Cup competition next week.
Out-half Miah Nikora is also set to return either this week or next after suffering a minor groin injury in the lead up to the recent derby match against Munster.
Winger Fetu'u Vainikolo missed out on the last round of RaboDirect PRO12 action due to injury, but is set to return to the fray this week.
There were a few knocks picked up during last Saturday's defeat to Leinster. Winger Matt Healy, who made his debut at the RDS, suffered a hand fracture and is set to be out of action for three to four weeks.
Meanwhile, former Ireland flanker Johnny O'Connor also picked up an injury and his involvement this weekend is in doubt.
David McSharry and Michael Swift suffered knocks at the RDS, yet they have both been given the 'all clear' and returned to full training yesterday.
As Connacht face into a big month of games both in the PRO12 and Heineken Cup competitions, head coach Eric Elwood said: "This game against the Dragons is a vitally important one for the squad. We're side by side at the bottom of the table so this is a huge game for both teams.
"Obviously, with us at home, the pressure is on us to win it. The key thing is that we learn from the mistakes of the last two derby matches that we've had. And the main focus for us this weekend is about getting everything right ourselves to secure the win."
While Connacht achieved the double over the men of Gwent last season, they lost 14-3 to the Dragons back in November.
The Dragons have visited the Sportsground on nine previous occasions and won only once, 32-14 in May 2004 on their first ever visit to the Galway venue.