Even if Patti expressed some interest, I don't think Arthur Laurents would allow it. I wouldn't put it past him to include such a clause in his will. Even in death....
"Noel [Coward] and I were in Paris once. Adjoining rooms, of course. One night, I felt mischievous, so I knocked on Noel's door, and he asked, 'Who is it?' I lowered my voice and said 'Hotel detective. Have you got a gentleman in your room?' He answered, 'Just a minute, I'll ask him.'" (Beatrice Lillie)