Tuilagi suffered a groin injury early in England's defeat to France on the opening weekend of the tournament, while Slade has been out since sustaining an ankle injury in December.
The centres trained with the Rugby World Cup runner-up o and could face joint-leader Ireland this weekend.
"Manu trained fully so should be in contention for selection. It's good to have a quality player back," England coach Eddie Jones said. "Slade also trained so we have just got to monitor his progress. He has a positive chance. He's a quality player. This gives us more options."
One player who will play no part is prop Mako Vunipola, who flew to Tonga and is not available for "family reasons".
Jones says England is well stocked to cover for the absence of the British and Irish Lions star, with Joe Marler and Ellis Genge vying for a start.
"Mako's a quality player but we are lucky we are blessed with two outstanding loosehead props in Joe and Ellis, so we can recover the loss of Mako," Jones said. "But it's disappointing to lose him."
Genge scored the winning try in a battling 13-6 defeat of Scotland before the rest weekend.