If a team would "like" to trade a player, it's very likely that the player's value is nowhere close to being at its peak. In fact, the value of that player probably already peaked long ago. And I bet the team didn't want to trade that player then.
It's not that teams don't ever trade a player at peak value. Oftentimes, a team has payroll limitations and a productive player's future earning projection does not fit into their budget. Rather than wait until the player is close to free agency, they will make a trade with two or three years left of team control in order to get the best possible return.
A bad team without much help on the way might also trade one of their players with the most value to help restock the farm system or bring some young talent to the major league roster.
In either case, the team did not "like" trading one of their best players. It just became necessary.
Now back to those players whom a team would not only "like" to trade, but would also "love" to trade and would even pay a big chunk of the salary and take only a fringe prospect in return to do so.
Whether it's a player not living up to expectations of a big contract or just not being as good as a younger and less expensive option at the same position, each team normally has some players whom they would like to get rid of, and hopefully, get something in return.
Here's one player from each team who is currently being displayed on the "sales rack."