Van Persie was ruled out for six weeks after suffering a knee injury in the UEFA Champions League win over Olympiakos last month.
The Dutchman returned to light training last Friday and he could be in contention to face Sunderland this weekend if he comes through this week's training unscathed.
United interim manager Ryan Giggs admits they will assess Van Persie's fitness this week before deciding if he will return to action against Sunderland.
"We'll just have to wait and see how he goes this week," Giggs is quoted as saying in the Daily Mail.
"He came back last Friday and he trained well. He just needs to work on his fitness now so, yeah, he looked great."
The news of Van Persie's fitness will come as a boost to Holland as they will be hoping the striker will be back to full fitness ahead of this summer's World Cup finals.