The Portuguese trainer wants the 30-year-old midfielder to extend his deal with the Spanish champions until 2016
The 30-year-old midfielder joined the Spanish champions from Premier League side Liverpool in 2009, initially signing a five-year contract that ends in 2014.
Currently, there have been no formal negotiations between the two parties, although Mourinho, who himself extended his contract until 2016, wants Alonso to do the same, as the Portuguese boss views the Spain international as a key element in his project.
Nuri Sahin was signed initially as Alonso's replacement but the Madrid coach wants the Turkey international to continue learning alongside the Spanish veteran.
The report also states that no time frame has been decided to resolve the issue, although Los Blancos are eager to tie down the midfielder.
Real Madrid ended the Primera Division campaign as champions, nine points ahead of Barcelona.