Tommy Pham
We've already heard Tommy Pham's name connected to the Cardinals, and with the White Sox looking to cash in on any talent they can by this deadline, his name will continue to be attached to St. Louis until he is actually dealt.
In 52 games with the White Sox this year, Pham has posted a .266/.342/.372 slash line, good for a 106 wRC+ and 0.3 fWAR thus far. He's been pretty solid for a terrible Chicago team, and we've seen Pham have the ability to take his game up a notch when he's playing for a competitive team (see his time with the Diamondbacks in the second half last year).
Pham, like Grichuk, is a former Cardinal and had interest in returning to St. Louis this past offseason. It's a bit odd that the Cardinals did not try to sign Pham after figuring out Edman would be down for some time, but they never anticipated Edman being out as long as he was, and Pham wanted playing time. Well, he should get that in St. Louis now.
Pham has been awesome against lefties this year, slashing .244/.382/.422, and has been playing center field with the White Sox as well. That would really help with roster construction for St. Louis, as they'd be able to move Edman around to second base, sit Gorman, and have Pham play center field, or just have Donovan play second, Pham in left field, and Edman in center.
Pham is also another guy who will be a free agent at the end of the season, so the price point should be a lot lower than others on the market.