New Orleans Saints general manager Mickey Loomis shot down the notion Wednesday that the Saints and tight end Jimmy Graham will aim to strike a new deal by the middle of this month.

A report by Pro Football Talk last month cited a source as saying the two sides would try to reach a long-term contract agreement before the April 22 deadline for Graham to file a grievance over his franchise-tag designation. Graham was officially designated as a tight end, though it’s expected that Graham and agent Jimmy Sexton will file the grievance to argue that he should be considered a wide receiver based on where he lined up most often last season.

“Look, I’m always optimistic. But there’s no deadline here,” Loomis said when asked if that April 22 date was being used as a target.

Loomis, who spoke to the media while attending LSU’s pro day, declined to give any specific updates on how talks are developing with Graham. But he seemed to indicate that the pace hasn’t picked up much since the Saints first placed the franchise tag on Graham more than a month ago.

When asked for the most rational way for fans to look at the situation, Loomis cracked, “Well, when does training camp begin?”

“I don’t have an answer for that,” Loomis continued. “That’s a two-way street. You know, you guys [in the media] have been through this lots of times. I think all of us would rather have things done sooner rather than later, but it doesn’t always happen that way. So we’ll keep going, well keep at it in the process. Obviously we want to have Jimmy Graham on our team when training camp begins, and I am sure he wants to be with us.