There appears to be a misconception about what attracts an agent. I've seen some advice out there suggesting authors submit to small presses to get a contract and then hunt down an agent to negotiate for them. To be clear, you can do this. Some agents think this is tacky. I think you need to do what feels right for your career. That said, you need to understand how the business works and the potential advantages and disadvantages of taking this route. Because honestly, a contract in hand is not the golden ticket that many authors think it is. Here's why:
If you come to me with a contract, the first thing I'm going to do is look up the publisher. Chances are, it's a small press that I haven't heard of (there are hundreds of these). Many authors mistakenly believe that this offer for publication gives their book a stamp of approval. And it can, but it can also mean diddly squat.
There are some truly wonderful small and indie presses out there. Seriously, some of these guys put the Big5 to shame with how wonderful they are to work with. And then there are others. Just like anyone can hang a shingle outside and claim the title of agent, anyone can set up a small press. Some of these guys will literally take anyone. They operate on a system of quantity over quality, pumping out hundreds of books a year with very little editing and bad covers. Without investing a lot of time in research, unless I've heard of the publisher, I have no idea which type your offer comes from.
If it's a bad publisher, I'm probably going to pass on representing your manuscript. Keep in mind here, this isn't based on the book at all. I'll pass, because a contract in hand from a bad publisher is a no-win scenario.
If I did sign you, I would have to advise you not to sign the contract. No contract is better than a bad one. I have to assume that isn't the only publisher you submitted your book to, and that seriously limits who I could submit to, hurting our chances to get another contract. Finally, there would be an unnatural pressure to sell the book quickly, because I advised you to turn down a contract in hand. Even though the offer was so bad it would have taken your book nowhere fast.
There is no way to win in a scenario like that.
Now, let's say the contract in hand was from a good publisher. If I signed you, I will spend hours working with the acquisitions editor to negotiate your contract. Even good contracts need to be negotiated. Because this is a small press, there probably isn't an advance or it is very small. Because of this, I probably won't see any compensation for upwards of 18 months. Now, that may seem cold-hearted. In fact, I can hear the shouts of "See, all agents are in it for the money". To that I ask, would you voluntarily go in to your office job without the promise of a paycheck at the end of the week? I love what I do and I adore books and authors, but coffee, liquor and sweatpants are not free.
Yet, despite all these potential negatives, I have taken on clients who come to me with a contract and I will continue to do so. If, and this is a big if, I love their work. Anytime an agent takes on a client, it's with the understanding that we might spend hours (and hours) of work on a manuscript, but not be able to sell it. That's why it's so crucial that I really love someone's work to take them on as a client. If you come to me with a contract, even one that is unlikely to earn me much money, I will sign you if I love your work so much I can't stand the idea of another agent getting their hands on it.
And really, that's what you should always want from your agent.