Boss Adams has yet to lead United to victory after seven games in charge and has brought in old mate Bassett, 66, who spent seven years in charge at Bramall lane in the late 1980s and 90s, to help turn things around.
Adams said: "He's back because there's not enough hours in the day for me. I've found the club bigger than I thought and his experience and the way we work together, as we've done before at Leicester and Nottingham Forest, will be valuable to me.
"When you're manager at Port Vale you probably get three calls a day and one of those is from the wife asking me what time I'm coming home for my tea, but when you're struggling at the bottom of the table and trying to organise scouting, talking to other managers, worrying about travel.
"There's a lot of aspects to management other than putting 11 lads out on a pitch on a Saturday. Harry will come in and work alongside me, we'll talk about tactics, players and what we do on the training ground.
"I'm not bringing him in to take the pressure of myself and he's not a threat to my job. It's something I wanted to do, the board have bought into it and we welcome him back."