Harper is definitely out after tearing a hamstring last week, but prior to Saturday Magpies boss Sir Bobby Robson could safely call upon Given.
However, the keeper picked up neck and knee injuries during Republic of Ireland's draw with Russia on Saturday and is a major doubt for the trip to Goodison Park.
"Shay hurt his neck and also aggravated a knee injury but hopefully he isn't too bad," Republic boss Brian Kerr said on Sunday.
If Given fails to shake off his knocks, Magpies chief Sir Bobby Robson may hand Tony Caig an unexpected Premiership start.
Former Hibernian shot-stopper Caig has yet to make a senior start for Newcastle, but could be thrust into the limelight if Given fails to prove his fitness.
Meanwhile, Magpies starlet Calvin Zola Makongo is hopeful his loan stint at Oldham will stand him in good stead for the future.
The Magpies sent the youngster to Boundary Park in a bid to boost his experience, and the forward is hoping to secure some regular playing time in order to catch Robson's eye.
"The gaffer sent me away to get some experience, so hopefully I can get a few goals during my time at Oldham and then when I go back to Newcastle hopefully I'll be nearer the first-team," the centre forward said.
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