The full-back has struggled with a foot injury since early in the 2020 campaign and did not play at all last year, after suffering a recurrence in pre-season.
Agar said Walker has a chance of being involved when Rhinos visit their dual-registration partner club Featherstone Rovers on Sunday, but may be given an extra seven days, until Leeds play Bradford Bulls at Odsal.
“I am pushing for Jack to play, but it may be the week after,” Agar said.
“We will wait until later in the week [to decide].
“He is not far off, I am not putting [any deadlines] on Jack, when we feel he is ready we will give him a game.”
Tongan international winger David Fusitu’a, signed from New Zealand Warriors, will have to wait for his first Leeds appearance.
Agar said: “He has had 10 days off with Covid, that has set him back a bit and he has only had three training sessions.
“We need to get him a bit closer to match fitness, we are not rushing him.”
Team captain Matt Prior did not figure in Rhinos’ opening pre-season game against Wakefield Trinity on Boxing Day.
“Matty, as an experienced player, is in good nick,” Agar explained.
“We will save him for our last trial game, against Hull.”
Forward Rhyse Martin, who was also left out of the team to face Trinity, will be in the squad on Sunday, Agar added.
Rhinos were close to full-strength against Wakefield and it is likely to be a similar squad this weekend.
“We will go with a relatively strong team,” Agar said.
“We have got to see how we get through the week, but we will probably roll around with the same side.
“We will give the half-backs another opportunity to play together and we’ll probably take a big squad, but a strong one.”
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