The defender was replaced by James Tavernier in the 56th minute of Saturday's 2-2 draw with Reading after pulling up and signalling his inability to continue.
With club captain Fabricio Coloccini already in the treatment room with a hamstring injury, the loss of the 26-year-old signals something of an injury crisis for the Englishman.
"I'm not sure [Taylor's] completely out of Sunday, but he won't play Thursday. It's a calf strain," he told the Shields Gazette.
"I don't think it's really bad, if I'm honest, but it might keep him out for the rest of the week.
"It's an area where we're not strong at the minute, with Colo being injured as well. We'll have to see what we're going to do for the Bordeaux and Man United games."
Pardew remains convinced, however, that James Perch can continue to deputise at centre-back, despite his sloppy showing alongside Mike Williamson against the Royals.
"I actually think we've been defensively solid all season. I think that's [Saturday] the first game where we've really been got at and I think that was mainly a result of having to take a centre-half off at that time," the Magpies boss, recently rewarded with a new eight-year contract, told The Northern Echo.
"For Perchy to have to go from right-back to centre-half is a difficult move. He just got caught out in a five or six-minute period, but he will be okay [against Bordeaux or Manchester United].
“He's been brilliant when he's played there in the past and I have no worries about him."