Alonso has emerged as a target for Louis Van Gaal following United's opening day loss to Swansea.
But with a move for Vidal still in doubt and Strootman not expected to be fit until later this year, Alonso could make sense as a stopgap measure.
Real were said to be unhappy that the Spanish international had returned to preseason having lost significant weight during the summer.
And it has even been suggested that Real could offload Alonso in an attempt to ease their midfield logjam.
For the big stories and the banter follow us on Twitter: @tribalfootball