but she never did.

When he, of course, discovers that his new neighbour, Nick, is related to her and knows Jordan Baker, a regular attendee at his parties, he sees it as an opportunity to finally make contact. He calls Jordan inside and probably, on this occasion, only wants to know more about her and Nick. It is, in all likelihood, only much later that he asks her to speak to Nick about arranging a meeting with Daisy. Daisy, obviously, must be unaware of the purpose of this arrangement, which is for him to 'accidentally' meet her at Nick's house.

One may question Jay's indirect approach and assume that he is cowardly. Why couldn't he approach Nick directly and make the same request during the few opportunities he had to do so? The answer probably lies in the fact that his ideal of reuniting with Daisy and the realisation that he now has a chance to succeed are so overwhelming, that he is afraid of being directly confronted with failure. It would be better for Jordan to soften Nick up and ensure, at least, a modicum of success since it seems as if Nick and Jordan share some sort of closeness.

It is clear that everything had to be carefully planned, which explains the delay in Jordan actually making the request (in chapter four) after she had given Nick the history of Jay and Daisy's association.

“He wants to know,... if you’ll invite Daisy to your house some afternoon and then let him come over.”

Jordan also confirms Gatsby's fear when Nick asks whether it was necessary for him to know all this detail before Gatsby could ask him such a little favour. She replies:

“He’s afraid, he’s waited so long. He thought you might be offended. You see, he’s a regular tough underneath it all.”

Nick accedes to Jay's request and brings him a step closer to realising his dream.  

The plan that Gatsby has devised is one that will put him so much closer to the goal of all of his dreams: to be reunited with his Daisy once more. He has discovered that Nick, apart from being his neighbour, is also Daisy's cousin, and so he believes that this is something he can use to arrange a secret meeting between Nick's cousin, the object of his affections, and himself.

Gatsby, however, is a cautious man. Having observed the link that there is between Jordan and Nick, he decides to try and get her to do his dirty work for him rather than approach Nick directly. He presumably feels that such matters are left to the more subtle approach that women can adopt, and as he knows so little about Nick, Jordan will be able to work out whether he will be amenable to being used in this way.

The revelation of this plan comes in Chapter Four, which you might like to read for yourself to think about how Nick responds to this and what his opinion of Gatsby is as a result. Ultimately, however, Gatsby is successful in pursuing his goal through this means, and Nick does organise a meeting between these two characters.