Barker, 33, who captained Derby under Clough, has not played competitively since dislocating his knee and rupturing ligaments in March 2012.
He is set to start training with Burton after undergoing minor knee surgery.
"If we have room budget-wise and he is OK, then it is a no-brainer for us," Clough said.
"He is just a good post influence to have around with Championship experience. He is a good person to have around the football club.
"His treatment is going well and he is close to joining back in, so he is one that we haven't ruled out at all."
After taking nearly three years to recover from his horrific knee injury, Barker returned to play for Derby's under-21 side in February 2015, only to be released by the Rams later that year.
He has since been granted a testimonial year by the Championship club and has repeatedly expressed a desire to return to play professionally.
Clough says Barker is still capable of making an impact as a player.
"You want him to contribute on the pitch, but he has a lot more to offer than just on the pitch," Clough said.
"He wants to get out and play. There will be plenty of times this season with five or 10 minutes to go when we will need someone to come on and head the ball in our box.
"I cant think anyone better than him."

Duffy is the only nominee from outside the Premiership, having led the Ton to the play-offs and the League Cup semis.
Rodgers is targeting the domestic treble in his first season in Scotland.
McInnes's Dons have reached two cup finals and are second in the league, while Thistle achieved a top-six spot.
Celtic striker Leigh Griffiths praised Rodgers for his "exceptional" man-management skills, adding: "he's different to what I've had before.
"He's very straight down the line. He tells you why you're not playing. His attention to detail in everything we do [was evident] from the first day he came in.
"We have progressed as a team and grown in stature and we're showing everyone what we're all about now. The only way we're going to go is forward."
Griffiths added: "If I had to choose one of the other three, I'd go for Alan Archibald.
"His Thistle team came here a few weeks ago and played really well to get a point. With the chances they had, they could maybe have won the game.
"With the budget they have and the way they are playing, they deserve to be in the top six."
The winner will be announced at PFA Scotland's annual awards dinner in Glasgow on Sunday.
Former Derby County defender Shaun Barker will be offered a deal at Burton Albion if he can prove his fitness, says manager Nigel Clough.
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Scotland's managers have nominated Aberdeen's Derek McInnes, Brendan Rodgers of Celtic, Partick Thistle's Alan Archibald and Morton's Jim Duffy for the manager of the year award.