You only get loans from other teams during trades - they have to loan out the money in order for you to take in the money. So, you will have to get your team legal in order to make this transaction stick.
Full disclosure, the site will not make you cut a player if you decide to keep your team in an illegal state for the last few days of the season, but you’ll be in violation of Rule 1a and be open to punishment from your commissioner / league.