Hi there, I think there would be a couple of factors.
There is a big difference between actual contracts, and offers/possible work.
Also, have you done your research on these Libraries to make sure they are active enough to make it worth your while? (I cannot tell you how valuable it is to read ALL of the replies on a library in the “Access Music Library” section!!)
For me, I have my Top-Tier Libraries that get priority, and then mid-tier.
When I “was” looking for new libraries I would stay in contact with them, and update them periodically. I would then be able to see if there was a rush, or if they are looking to get a product/style like the one(s) I submitted out into the marketplace..
I wish you much success!!