From Charles Leerhsen's biography “Ty Cobb: A Terrible Beauty”:  

Clark Griffith of New York had hinted that [Tigers new manager Hughie Jennings] might want to make a swap. When Hughie heard back from the Highlanders the next day, however, they were offering only Frank Delahanty, a .238 hitter, a proposal that was either, as Hughie said, “a humorous effort,” or an indication of just how wary some people were of young Tyrus.

This was before the start of the 1907 season. Cobb, who at this point was 20 years old and had played 139 games over the two previous seasons (batting .293), would go untraded. There'd been strife on the team, according to Leerhsen, because some of the other players, northerners mostly, disliked Cobb, who kept to himself, had airs, read books, and was, you know, good. They hazed him for the better part of a season. To some, Jennings mostly, it would just be easier to get rid of the kid, but Tigers' business manager (and eventual owner) Frank Navin liked Cobb and squelched any deal.

Over the next 13 seasons, Cobb would win 12 batting titles, lead the league in OPS nine times, hits eight times, runs five times, RBIs four times, and stolen bases six times. The Tigers would also win three straight pennants (but no championships).

The Highlanders, soon to be the Yankees, would have to wait out those 13 seasons before they began their turnaround.