I expect that Alexandrov and the Blues will eventually agree on a league minimum deal that is either 1 way or pays him a $400k+ AHL salary.
For the player, he has to see the writing on the wall that he isn't a lock to make the NHL roster. Last season went very poorly for him. While the team let a few bottom 6 guys walk, they also brought in 3 legit NHL-caliber bottom/middle 6 players and extended Kapanen at bottom 6 money. The result is 12 forwards on 1 way deals, plus Neighbours (roster lock), plus Bolduc (highly likely roster spot), and all the other prospects coming to camp to try and earn an NHL job after another year of development. On top of those 14+ forwards to worry about, it is looking like the team very well might carry 8 NHL D, which would take one of the 'extra' forward spots on the roster. Securing a good AHL salary just has to be a priority for him even if he is extremely confident about earning a job at camp.
Obviously the team wants to minimize what they spend on him. However, I think he's a good enough player and has enough promise that it is worth paying him a few hundred grand to play in the AHL if that is where he winds up. It's a (small) disincentive for a team to pick him up on waivers and it keeps him open as an option when injuries hit.
I think a league-minimum NHL salary with an assurance of good money in the AHL just makes too much sense for a deal not to get done.