Martin has just completed a successful three-month loan spell at Plymouth, who wanted to keep hold of the 20-year-old.
Martin said: "I spoke to Sir Alex on Wednesday and he told me of the interest. There were a few other clubs interested, but it is good to know a big club like Sheffield United is interested in me.
"Plymouth wanted to extend my stay, but the decision was made by myself and Sir Alex. I will work hard but hopefully I can bring a bit of flair, pace and energy."