Too many of these deals are looking at making a bigger trade than the Blues realistically need. We'd be looking for a middle-6 guy who can chip in, and we don't really need term.
Nash only makes sense if he is very cheap, and that isn't a first+. He has averaged 45 points per 82 games since the start of the 2015/16 season, he has had injury issues and he hasn't started this season particularly well. No incentive to pay a price for him when an in-form rental would likely be cheaper.
We have Tarasenko, Schwartz, Steen, Schenn, Berglund and Sobotka signed to multi-year deals. Fabbri will be back next season in some role. Stastny or a replacement centre, and then a glut of prospects. Adding another long-term piece doesn't make sense.
The early Bozak for Berglund proposal? I'd do that.
Or as STLBLUES44 suggests, going after someone like Stempniak as a rental makes a lot of sense.