You can also offer a no-trade clause.
If you have the money and the minor-leaguer is worth it, offer a major-league contract. Assuming the player has options, you can keep him in the minors, and then his salary will revert to $55,000 or so the following season.
A few seasons back, we had a bidding war for a C who was close to major-league ready defensively (and outstanding) and whose bat suggested he'd be a decent platoon hitter. The bidding went to close to $1M, even though he remained in AAA for another 1.5 seasons.