I don't think Miami would trade for him, since he will be a free agent this Tuesday. I don't think they would want to give up more picks and another big contract. I think they will take their chance with him on the market and just simply hope their offer beats everyone else.
Still though, a trade would be possible even though he hasn't signed his tender. If Miami and St. Louis worked out a trade, then Atogwe would likely sign it so he can get traded. Miami then would turn around and sign him to a long term deal. That is exactly what happened with Brandon Marshall. He signed his tender with the Broncos, the next day he was in Miami inking a big contract. Marshall only signed his tender because he knew he was getting traded.