Davies, who has played in all eight Solheim Cups, is at number two in the rankings and the top seven will be guaranteed selection at the end of the Ladies' Finnish Masters on Sunday.
But it will be a more anxious few days in America for fellow Britons Catriona Matthew and Karen Stupples as they have to rely on wild-card selections for Europe's defence at Crooked Stick in Indiana in two weeks' time.
Matthew is the defending champion in Ohio, is the leading Briton at number 17 on the LPGA money list and seems certain to be included in captain Catrin Nilsmark's chosen five. She was one of the heroines of the win in Sweden two years ago.
But Stupples, last year's British Open champion, has missed three tournaments with an ear infection and her debut is now in doubt.
Swedes Carin Koch, Sophie Gustafson, Liselotte Neumann, Norway's Suzann Pettersen and French player Karine Icher are the other wild-card hopefuls for Ohio.