It is understood that Rafael Benitez's side have already have a loan approach rejected by Liverpool and that Middlesbrough are in pole position to secure his signature on a short-term basis.
But Klopp will let him go as he is unlikely to start this season and the fee is enough to tempt Liverpool to sell the Anfield reserve.
GETTYRafael Benitez has admitted his frustration at the"crazy transfer window
It's added in the report that the England U20 global will be left behind on Liverpool's trip to Asia as part of their pre-season preparations in order to discuss his move to St. James Park, while Middlesbrough are also interested and will offer competition.
The England Under-20 global recently helped his nation's youth side to World Cup success and is a highly rated talent.
Ojo made a pair of FA Cup appearances for Liverpool last season and had been expected to build on those next term. With plenty of experience in League One and The Championship, as well as worldwide experience, Armstrong could be a shrewd loan signing.
Newcastle could do with an additional option in the wide area ahead of next season to provide completion to the likes of Matt Ritchie, Christian Atsu and Rolando Aarons. Benitez is keen to show his intent following Newcastle's return to the Premier League and splashing out £10million on Ojo would be an incredible risk.