Baker sure looks like a good starting QB and those are in high demand. He has also been screwed by being on lousy teams and he may want to be able to choose a good spot to land.
Only way I can see him staying is if the opportunities out there are all with crap teams and if he thinks it would be helpful for his long term development to stay with the Rams. Stafford will be the starter and there will be no competition. I am not even sure the Rams can pay him the good backup QB rate of 6-8Mil.
If I am Baker I am looking for a 3 or 4 year deal at 25Mil +. I am also looking for a team with a good offensive scheme, a decent line and good WR/TE. If he finds an opportunity close to that he really has to take it. We will get a 3rd round comp pick if he finds that type of fit .
Anyway the odds of him staying as a backup for next season are very low.