Its very possible they do, but I'm sure they would rather trade him. Kupp is a $17M cap hit if they trade him now. He carries a $21M cap hit as a post june 1 cut. If they were willing to eat just a little bit of his money this year why not do a similar deal like Christian Kirk and Houston? Float them a late pick and you get Kupp at probably a slightly inflated number for this year, but you're really only committed to him for 1 year. Let him hit free agency and you have to come up with signing bonus money, probably float him a multi year commitment, etc. You're absolutely right that they can get him at a cheaper AAV as a free agent, but you have several other teams that will be bidding up how much of guaranteed, number of years etc.
Personally if LA is willing to play ball (and they might not be) I wouldnt hate just flipping him for a late pick and cutting out the free agency BS.