There's been occasional rumours, but I generally assume that all the top clubs are at least keeping an eye on most of the top players who may be open to moves, and that pretty much all of us will be linked with every vaguely plausible Tom, Dick and Harry at some point in the window.
From what I've heard about how clubs do business, they conduct long term scouting and analysis of a long list of players, and have preference lists so if they can't get their top choices they have backups they can move on to. I think it's safe to assume Mahrez wasn't a 1st choice, but then again this stuff is always going to be complicated by players and their agents changing their minds and requesting late moves or whatever.
I certainly wouldn't consider a good player who would have seemed a totally logical buy at any point to be a 'panic buy'. I'd reserve that for things like the Djilibodji transfer a few years back where it genuinely did seem like we'd gone 'OMFG we can't get Stone and need basically anyone!!'.