The bullish midfielder has been sidelined for the past month with the ailment, and was put through his paces in the Giants' final main session on Thursday to prove his fitness.
Taranto remains a chance to return to action this weekend, but frames as a stronger chance to do so through the club's reserves.
"He's more than likely potentially VFL more than AFL at this stage but yeah, he's got to complete the session today."
McVeigh will consider bringing his key defender back into his 22-man side, but will be needing to consider how it could impact in-form forward-turned-defender Harry Himmelberg this weekend against the Western Bulldogs.
Haynes has battled illness in recent weeks and hasn't featured for McVeigh's side since Round 9.
"It makes a difficult selection process for us and how we go about it," McVeigh said.
"We've got to take into account the opposition and what they can bring. So you know, there'll be a pretty robust match committee today.
"Do we reset Harry and move forward? Do we play him somewhere else? What does it look like? We've got some things to discuss."
Should Haynes face another week in the reserves, he won't be the only senior AFL-listed backman to line up against the Suns at Metricon Stadium in the VFL on Sunday.
McVeigh confirmed veteran Phil Davis will make his return through the VFL on the weekend, with the club looking to get "more work into him" before the club's reserves have their bye next week.
Davis has been deemed fit to play after working through rehab on a hamstring strain suffered in Round 2.
McVeigh's key position stocks have taken a hit over the past month, with ruckman Braydon Preuss battling the flu across the past month.
Preuss was among the senior Giants to feature in the VFL last week, and is being considered for selection this weekend.
"He's definitely a chance, he's in the mix," McVeigh added.
"What people have got to understand is that Braydon was quite ill prior to the bye. He was struck down by the flu more than probably some of our other players unfortunately.
"It took him sort of 12 or 13 days to get over that. He wasn't able to train, he wasn't able to play. Then slowly but surely we were able to get him into training and play his first VFL game over the weekend."
Haynes, Preuss, Jarrod Brander and Cooper Hamilton are all eyeing spots in McVeigh's side to face the Bulldogs, which will see at least two changes after injuries to Harry Perryman (ribs) and Matt de Boer (concussion).
Both Brander and Hamilton are among those in the mix for this weekend as McVeigh looks to fill voids in his engine room.
"He certainly is someone that we're considering this week," McVeigh said of Brander.
"Off the back of 34 possessions, uses the ball really well, can play half-forward, can play wing. So we've got some flexibility on there.
"Cooper Hamilton, we know what he can do. We know at the moment that he can play as a deep defender and really shut out a small forward if we need that. He can actually tag if we'd like him to and he can play forward.
"I'm not really capping or putting any roof over any player where they can play and what they can do. I'm open to everything to be quite honest."
The Giants will host the Bulldogs at GIANTS Stadium at 7:25pm (AEST) on Saturday.