Do you have access to the diplomacy screen? If you do, you're a kingdom, if it's greyed out you're a solo clan. Also I don't think you can have that dialogue with anyone if you're not a ruler, I think it's a different question then.
They will refuse if you're chances are too low so it doesn't waste you time on the dialogue you can't pass (or can't pay them to join).
A vassal consider's many things as to if they will possibly join you( in rough importance order):
1 Do they have a fief? If they do it becomes much more expensive and unlikely they will join you. If they don't it's much easier/cheaper.
2 How much power do you have (parties and garrisons= Power) compared to the faction they're in? The bigger you are the better.
3 DO they like thier king, do they like you? If they have low relations with the king and good relation with you, it help you, if not.... the opposite
4 Finally, how much money could you pay them to join? The worse you are in the 1 2 3 tips the more they would want to join you and if you don't even have the amount they would want, they won't give you the dialogue to try.
Here is formula posted by
@mexxico recently
1.6.0 formula was opponent directly rejecting if needed money is > 20% of player's money at 1.6.1 it will be 33% + 250K. Also we are changing dialog opponent says while rejecting your offer it was not clear enough why he rejects.
So that's an idea of how much money you need to have! In general a fief-less clan will join you for say 250K or so, but it could still be more or less depending on you power level and relations. If you have just 1 fief and thier faction is big a strong, they may still want too much to join you.
Hire mercenaries and try to expand your faction (creating fief-less lords by taking thier homes) will help you be more likely to get vassals!
If it turns out you're not a kingdom yet, consider using the solo clan status to take more fiefs before declaring a kingdom. Being a solo clan you can make peace and not have war declared on you, so you can focus on taking fiefs from 1 weak faction or such. This depends on using you 1 party to defeat enemies and take fiefs though, so it's not for everyone.