Just be honest and, as Kilisi pointed out, look out for yourself first. That means you should reach out to you contact right now. Assuming you don't get an immediate response you then inform your former colleague that you're actually also looking at your next career step and have already reached out to your contact. Of course you only did so after he made the request, but that's a harmless white lie to avoid having your former colleague think you got the idea from him.
You don't have to do so, but it will likely go over better if you can speak in the past tense here.
There's some risk that your former colleague will still assume you only decided to talk to your contact after hearing from him, but there's nothing you can do to control that. You should simply be transparant and open to minimise that possibility and preserve the relationship.
Now, as for what else to do here, that's something for you to decide. If you're comfortable passing along your former colleague's details to your contact as well, and potentially lose a job to him, you can still do so. It would be a kindness but you have no moral obligation to do so. You should also factor in whether your former colleague will reach out to your contact or the company at large if you don't make an introduction, in which case you have little to lose by introducing him as well. But if there's no posted vacancy that all becomes muddier.
An example script for your colleague:
[As you know] I'm also looking [to move on / for a new job] and I've actually already reached out to X to discuss a possible position on his team.
Given that, I think it would make more sense if you apply to the company / contact him yourself. [I'd be happy to connect you two via mail though if that would help.]
I'm happy to introduce you as well since I know you'd also be a strong fit for their culture / team, though I understand if you want me to limit my involvement since we'd likely be pursuing the same position.
Regardless of which avenue you take, because you're essentially applying for the same job you'll probably want, and will be expected to, limit your further involvement. Some people might be comfortable asking the both of you to speak about your experience working with the other as a form of reference, though most won't given the innate awkwardness. The key stance to take throughout whatever process follows is simply to be professional and don't sabotage your former colleague. You don't need to sing his praises quite as much as you would if you were asked to be a reference for a job you weren't in the running for but speaking favourably of his strengths if asked is a good sign of professional maturity.