Gardner has 163 career stolen bases and has swiped more than 45 twice. Ellsbury has 245 career stolen bags and has stolen 50 or more three times, leading the American League on all three occasions.
The Yankees' franchise leader in the category is Rickey Henderson who stole 93 in 1988, and while it's unlikely either Gardner or Ellsbury unseats Henderson, there are two records they could help break:
(1) The Yankees team total for stolen bases during the live ball era (after 1920) is 163 in 1976.
(2) The Yankees have never had a pair of teammates each swipe 45 or more bases.
Gardner and Ellsbury have combined for 10 stolen bases (two caught stealing) and the Yankees have 13 stolen bases as a team as of April 20.