Southerngirl
I believe you are thinking of Francis Tumblety. He certainly was being actively sought and was tracked across the Atlantic. Then, rather suddenly, the police appear to have dropped their interest in him. I would have to dispute the term "evidence" when relating to him and, indeed, the overwhelming majority of Ripper suspects, contemporary or otherwise. "Supposition" might be a better term.
It's all a bit of a parlour game now. Well, it would be, if mountains of money weren't being made by dodgy books containing dubious "research." My own "likeliest suspect", for what it is worth, is Kosminski, who was one of the 3 men named in an 1894 document, 6 years after the killings were thought to have ceased. One of the senior officers on the case, Donald Swanson, appears to have concurred with this (or, rather, I concur with him) and in the absence of any damning evidence against any other suspect, I would rather go with what the senior officers of the time believed than what someone comes up with 100 years after the fact. Still, each to their own opinion!