The former Magpies shot-stopper is now on the books of relegation rivals Sunderland.
The Magpies were already without regular number 1 Tim Krul for the rest of the campaign when second-choice shot-stopper Rob Elliot suffered a serious knee injury playing for the Republic of Ireland.
According to the Times, Elliot's absence has prompted Rafa Benitez to scour the free agent market for replacements, though Harper is tipping stand-ins Karl Darlow and Freddie Woodman to make the step up.
The 41-year-old, who spent 20 years a Newcastle player, told TalkSPORT's Alan Brazil Sports Breakfast show earlier: "Darlow’s played a lot more league action that Freddie. But Freddie’s got a big, big future. He’s done really well and he’s got a fantastic attitude: really driven; works his socks off.
"So it’s a big call, because people assume he (Benitez) will go with Darlow given his experience. But Freddie can handle it, believe me, and he is destined for a big future. Whether you thrown him in at this time of the season, that’s not my decision."
Darlow, who arrived at St. James' Park in 2014 but was allowed to continue his development at Nottingham Forest until the summer, has appeared just once in the Premier League but failed to cover himself in glory.
The 25-year-old was arguably at fault for Darren Fletcher's winner in December's defeat to West Brom, but Harper is certain he'll recover.
"It's tough," he added. "You can play in the Championship for as long as you want but you come up into the Premier League and it is quicker and the quality is a lot better.
"He'll certainly benefit from the experience he had at West Brom."
Woodman signed for the Magpies from Crystal Palace's youth setup in 2013, but is yet to make his first team bow.
The 19-year-old does have some senior experience, however, courtesy of loans in the Football League with Hartlepool United and Crawley Town.