The Belgian stars said at a joint press conference on Thursday they are open to the idea but need to overcome scheduling difficulties.
"Obviously for the Olympics, it would be beautiful," US Open champion Clijsters said, adding 2012 also could be her last full competitive season. "It would be nice to go out in such a way."
Clijsters has never competed in the Olympics. Henin won a gold medal in singles in 2004.
The pair have admitted in the past they are not close friends, but before their exhibition match on Thursday, Henin said they were keen to compete as a pair in 2012.
"There is a real willingness to be there," Henin said as she prepared to play a match for the first time since injuring her elbow at Wimbledon. "We can already think about it. Everything is open to consider this."
Clijsters won the exhibition match in a super tiebreaker 10-5 after she won the first set 6-1 and Henin took the second 6-3.
Henin and Clijsters played doubles together at the highest level on one occasion, when Belgium lost to Russia in the 2006 Fed Cup quarterfinals. In 1999, they paired up twice in minor tournaments just as their careers were taking off.
They could face tough competition in 2012 from the 2000 and 2008 gold medalists Venus and Serena Williams, who, if healthy, will be difficult to beat on the grass of Wimbledon.
Clijsters' and Henin's careers have followed similar paths. Both reached the No. 1 ranking before retiring suddenly and then making a comeback.
The 27-year-old Clijsters was the WTA player of the year in 2010 after winning the U.S. Open for the second year in a row and four other titles.
Henin returned at the beginning of the season but had her encouraging comeback cut short at Wimbledon when she fell and tore a ligament in her elbow during a fourth-round match -- against Clijsters.
"For sure, I'm still not 100 percent," the 28-year-old Henin said of her fitness. "But if I realize where I came from, I am lucky and happy to be where I am now. I thought at some time, that I would never get back."
She plans to begin her preparations for the Australian Open by playing at the Hopman Cup at the beginning of January.