Hatch? Alexander? Cochran?
It's also claimed that this is a relatively low profile Congressional Republican, which coupled with the fact that it's a Senator should trim the list down quite a bit. Probably someone newer to the Senate than the old warhorses you listed (counting Alexander's pre-Senate years in the limelight as Senate service equivalents here). And a man. And someone from a state with several Republican Representatives.
So the contenders are
Blunt (R-MO)
Boozman (R-AR)
Burr (R-NC)
Chambliss (R-GA)
Chiesa (R-NJ)
Coats (R-IN)
Corker (R-TN)
Flake (R-AZ)
Graham (R-SC)
Isakson (R-GA)
Johanns (R-NE)
Kirk (R-IL)
Moran (R-KS)
Portman (R-OH)
Wicker (R-MS)
...that's before starting to take ideology into account, which really rules out a number of them.