The Mirror says Olisie, who can act as a number ten or on the wing, has emerged as one of the best players outside the top-flight and is wanted by a host of teams – including Liverpool.
He apparently has a release clause of £8million in his contract, though those claims have been disputed.
And on Tuesday night he suffered a potentially long-term injury after going down with a knock on his shoulder.
Reading boss Veljko Paunovic said: “It's a shoulder injury which has to be assessed tomorrow. It could be a long-time injury."