McKay, who has just one year remaining on his current deal, turned down the Ibrox club’s initial proposal in February and says there has been no further contact since then.
The 22-year-old winger has subsequently been linked with a move to Nottingham Forest, where former Rangers manager Mark Warburton has been promised substantial funds this summer by the club’s prospective new owner Evangelos Marinakis.
Caixinha has used McKay relatively sparingly since replacing Warburton at Rangers in March and says he wants to see a greater all-round contribution from the Scotland international.
“Barrie needs to wait [on a new contract],” said the Portuguese coach. “If he is waiting, then he needs to wait more for the club to come back to him. Barrie is a great guy and a fantastic footballer but we are assessing him and we will give him an answer as soon as possible.
“He has been more proactive in the last two games but I still want more from him. He’s been a very important player for the last two matches, scoring twice, as has Joe Garner. They are two players living a good moment and football is about good moments. We now need to extend that.
“What does Barrie need to do more? He needs to be more proactive. The game is a lot of phases and stages and I want all the players to be keen on the game. If things are not coming they need to look for it. When he needs to sacrifice, he needs to do that as well.”
Asked if he would look to sell McKay this summer if no agreement on a longer-term contract is reached, Caixinha replied with a firm “No” but then admitted he wanted to see a certain level of commitment to the club from any players he regards as key to his plans for the future.
“I just want players here that are keen to come here, that are keen to continue here and are here through the passion they feel for the club and the passion they have to win for the club,” he added. “Otherwise, if they are thinking about contracts, I think this is not going to be their place.”