The Poland midfielder is on a season-long loan from PSG, though there is no settled option to sign permanently.
But! reports ASSE were in advanced talks with Krychowiak before the Baggies' intervention.
St Etienne couldn't get a deal done in time due to the midfielder's wage demands, which were well outside their budget.
In contrast, West Brom had no such issues and were happy to deal in Krychowiak at the start of this season.
Meanwhile, Baggies boss Tony Pulis insists they've paid for defensive errors this season.
Albion sit one point above the bottom three after nine league games with a win.
But Pulis countered: “We've been our own worst enemies.
“We could be sat here with an extra six points easily and nobody would be criticising the three in the middle, the five at the back, the one up front or whatever.
“Looking back at the goals we have conceded, and how late they have been, it has been concentration or individual errors. That's what has cost us.
“I don't think it has been anything more than that.
“Even games, you look at Leicester, we have had opportunities to score more goals, and we haven't taken them, and then got punished.
“That's what happens. It sometimes goes for you, sometimes it doesn't, but you have to make sure the players keep a level head and keep doing the right things.
“We have left a lot of points on the pitch.
“I don't think the performances have been that bad, no-one has given us a hiding.
“Even at Brighton they scored just before and after half time which killed that game.
“We've shot ourselves in the foot more than anything else."