Alex, 34, has been a free agent since ending a two-year spell at AC Milan in May, reports Xinhua.
"I like him, he is exceptional. He would be very welcome but we are going to wait and see," Dorival Junior told Globoesporte on Sunday.
"We need to know if he is interested. It would be significant, but we can't talk about it now because we are focused on the rest of the current season," he added.
Santos are currently fourth in the Brazilian Serie A standings with 48 points from 28 matches, six points behind leaders Palmeiras.
Alex, who began his career at Santos before joining Chelsea in 2004, has been capped 15 times for Brazil since his international debut in 2002.
