Rutgers was asked to join the Ivy League and here's the source.
^ Several articles 1948-1956 in the The Daily Targum (Rutgers University's campus newspaper), located in The Targum, The Rutgers Targum and The Daily Targum (then printed weekly) Microfilm records (1) v.87-v.94:no.35 OCT 17,1945-APR 10,1953, and (2) v.94:no.36-v.104:no.58 APR 17,1953-DEC 5,1972 (2 rolls) and Walton R. Johnson Papers (1949-2001), Special Collections and University Archives, Archibald S. Alexander Library, Rutgers University, New Brunswick, New Jersey.
Now if you ask the Ivy League, their official response is "We have no records of any invitation being extended." Which is different from, "we never extended an invitation." My understanding is that the offer was conditional on Rutgers foregoing the state university/land grant designation which would have required them to split off the Ag school on Douglass Campus. RU said no thanks. So the negotiations probably never got past that point into more formal negotiations.