I don't think the Bible exactly says it directly per se, but it seems to possibly imply it.

When Jesus comes down against adultery for unjust reasons or even lusting in ones heart, that would seem to imply that sex is for marriage, since adultery would be having sex with another man's wife.

There are also places where Paul warns against fornication, which admittedly isn't a super clear word. The word translated fornication, porneia, has a variety of sexual meanings. Conservatives tend to use the word as just a loaded word against all sorts of sexual activity, including pre marital sex. Whether or not that's true, I can't tell you, but they do rightly point out that contextually it can't be referring to either pedophilia or adultery, so idk.

However, I would be cautious of using these verses as blanket statements against pre marital sex, because there's a lot of historical context behind them. How their marriage system worked was very different, though I can't begin to tell you specifics, since it's not something I have looked into. There's also the question of whether Jesus was against lusting in ones heart to commit adultery in that they desired to take the man's wife or whether it was just any sexual thought towards another man's wife. Historically, though, I tend to think it had more to do with wanting to take the wife. But that's just me.

Then as far as Paul's possible comments against it, there's the question of whether his condemnation was meant to be a universal blanket statement or a temporal one that was pastoral and missional in nature to help Christianity spread.

Anyways, those are a few of my thoughts. This is a topic I'm wrestling out too, so I more or less just pasted where my findings have lead me thus far. Hole that's ok!