The Crystal Palace duo are two of the most highly rated young attackers in the Premier League.
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Olise and Eze are being linked with moves to top clubs in the Premier League and abroad.
“We were really interested in Eze and Olise,” ex-Magpies chief Bruce told talkSPORT.
“We tried to chase the two of them. They were never going to leave London, though, and Newcastle wasn’t the Newcastle they are today, of course.
“They are two really exceptional footballers, Eze in particular. He has this natural ability which just comes across when you watch him.
“He has that ability to go past people which seems to be a bit of a dying art at the moment. He has got that in abundance. He really looks a wonderful footballer at the moment.”