I have a domain name that's about to expire in 3 days. I really do not want to renew it with my current registrar. Can I transfer it to Dynu?

i wouldn't do it. Why risk losing your domain name?

If you really do not like your current registrar. You should have transferred earlier. Waiting till the last minute, not a good idea.

Thank you both for the 'lecture'. I am actually looking for a solution here. Anyone can help?

You can transfer your domain name without any issue. Just unlock your domain for transfer and get the authorization code. Although domain transfer takes 5 to 7 days, it is well within the renewal grace period(normally it is up to 15 days). Actually you can even transfer your domain name after it expires. So unlock your domain name, get the authorization code and place an order for transfer. Simple as that.

Not true with all registrar. With good one, yes. With bad one like (redacted), no. If you do any change they lock the account for 60 days no matter what. I have a domain, expired, and no way to get it before it becomes free for purchase. Sometimes it's better to renew at the bad one, then transfer as soon it's technically possible. You have to buy an extra year at each registrar, but it's cheap compared with the trouble.