Many things link Wolverine and Deadpool. They're so linked, in fact, that Deadpool owes his healing factor to his fellow member of the Weapon Program. The factor has gifted both of them with many benefits. Nearly immune to almost all kinds of damage, significantly impeded aging, even resistance to some of the most powerful telepaths in the world. However, one power not often discussed, which both men would probably find uncomfortable to consider, is their potential to walk clone factories. Sever their body parts, sew several pieces back together, and voila. It's happened before.
The prime example of this is "Evil Deadpool." A deranged doctor obsessed with Deadpool managed to recover leftover parts of the Merc with the Mouth over years of stalking. She kept them in a freezer before Deadpool discovered them and promptly threw them away. This would come back to haunt the merc with a mouth as the parts thawed. Due to a combination of the strength of Deadpool's healing factor and the parts' close proximity, they merged. The result constituted an effective clone of Deadpool, one that literally stitched itself together. It's a horrifying way to replicate oneself and one that yielded obvious aberrations within Evil Deadpool.
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While Wolverine has yet to exhibit the same "constructive cloning," that doesn't mean he can't. For one thing, when it comes to Logan, there are years of adventures the X-Man can't remember and readers haven't seen. It is entirely possible that the cranky Canuck's pre-1940s life is rife with body parts reconstituted themselves into separate Logan-shaped people.
There's also the reality that, as stated earlier, Deadpool's healing factor is a derivative of Wolverine's. Therefore, it stands to reason anything Deadpool can do, Logan can do at least as well, if not better. Wolverine has survived injuries such as having all his organic matter burned away saved for his adamantium skeleton. Deadpool has even had his head lopped off and still operated his body from afar. Their powers allow them to defy the laws of nature. It resides in every part of their bodies and sometimes defies all reason to keep its host going.
If either one of them appears in the Marvel Cinematic Universe with their healing factor and full strength, fans could be treated to quite the sight. It's a gruesome sort of fun to imagine. Heck, both characters have starred in R-rated films full of some decidedly bloody violence. So what's a little body horror on top?
That's an enjoyable flight of fancy, and their bloodsoaked cinematic past does make it more likely to happen to them than, say, Ant-Man. Still, it is almost certain to remain in the fantasy realm, a hypothetical to be enjoyed by the gorehounds among us. First and most important, this is Disney we're talking about here. While the MCU has gotten a wider berth than their animated features, there are miles between the Snapture dusting and watching Wade Wilson's fingers reattach themselves to a severed hand.
There's also the problem of it being, simply, too much of a power. Even on the page, Logan and Wilson's healing factor has long since strolled past the line of "utterly ludicrous." Dropping a full-strength healing factor in the MCU will stick out like the most bullet-riddled of sore thumbs. Reducing the healing factor to something impressive but still manageable allows for reasonable stakes. Deadpool is more likely to come back silent with telescoping blades in his wrist than audiences are to see these healing factor clones.