The former Brazil midfielder is scheduled to hold further talks with Robson later this afternoon after impressing during a five-day trial last week.
Ze Maria, who has also represented Parma, Internazionale and Levante during his distinguished career, could even put pen to paper on a one-year contract before tomorrow's Championship fixture at Blackpool.
After watching his team climb to eighth in the table courtesy of Saturday's 3-1 win over Wolverhampton Wanderers, Robson confirmed: "We'll be speaking to him and his people again and providing we can come to some sort of arrangement then, yes, I'll probably take him.
"Nothing is certain yet but it's been good having Ze Maria here."
James Beattie scored twice as United claimed their second league victory this season during a dramatic match in front of 26,000 supporters at Bramall Lane, prompting Robson to suggest that his squad have learned the lessons of their defeat by Scunthorpe earlier this month.
"But how they are at Blackpool will tell me even more," he continued. "We are doing well at home and now we want to start going away from home."
The match also marked the return of Stephen Quinn and Gary Naysmith from injury while Robson also revealed that Lee Hendrie should be available when United travel to Crystal Palace next week.