The 20-year-old has caught the eye since arriving at Ashton Gate from West Ham at the beginning of March.
Millen has spoken openly of the need to strengthen an ageing defence in the summer and he revealed that Spence features on his list of potential transfer targets.
Out of contract at the end of the season, Spence and his agent are in talks with West Ham over a new deal and Millen is monitoring the situation as it unfolds.
"I've been pleased with Jordan and he is in my thoughts," Millen told the Evening Post. "But I don't want to be disrespectful to West Ham because he is still their player. We will have to see what division they are in next season because that will have a big bearing on what happens.
"West Ham are still negotiating with Jordan and his agent and I'm not sure what the future holds just yet. I've been saying for a long time now that we need to bring in more defenders to provide competition and right-back is one of the positions we are looking at."
Source: PA
Source: PA