Mr Obama told a news conference he was "aware of press reports" on the issue, but would not make a statement on it.
Hillary Clinton, due in Beijing later this week, also declined comment but said rights issues would be discussed.
Activists claim Mr Chen entered the US embassy in Beijing earlier this month, after slipping out of his home.
US and Chinese officials are thought to be in talks on his fate.
State Department spokeswoman Victoria Nuland confirmed that a
senior US official, Kurt Campbell, had travelled to Beijing, but
declined to say whether he was in discussions about the activist.
Mr Campbell, who arrived on an unscheduled visit, is believed
to be in highly delicate negotiations with the Chinese authorities.
The BBC's Adam Brookes in Washington says one of the options
on the table is for Mr Chen to go into exile, but he is said to be
averse to that solution.
Ms Nuland said Mr
Campbell's visit was to prepare for the visit by Mrs Clinton, the US
Secretary of State, on Wednesday. Both she and Treasury Secretary
Timothy Geithner are due in Beijing for the annual US-China Strategic
and Economic Dialogue - now expected to be overshadowed by the issue of
Mr Chen.
Ms Clinton said on Monday that she would raise the issue of human rights during her talks.
"A constructive relationship includes talking very frankly
about those areas where we do not agree, including human rights," she
was quoted saying by the Reuters news agency.
Mr Obama, meanwhile, when asked specifically about Mr Chen's
case, said he could only stress that "every time we meet with China the
issue of human rights comes up".
"We want China to be strong, we want it to be prosperous and
we are very pleased with all the areas of co-operation that we have been
able to engage in," he said.
"But we also believe that that relationship will be that much
stronger and China will be that much more prosperous and strong as you
see improvements on human rights issues in that country."
'Utmost restraint'
Mr Chen was placed under house arrest in Shandong province in
2010 after spending more than four years in jail for disrupting traffic
and damaging property.
He is thought to
have escaped the house where he was being held more than a week ago,
although the news only emerged at the end of last week. Activists say he
was then driven to the US embassy.
The activist, who has been blind since childhood, has long
been a high-profile figure and international rights groups have
frequently expressed alarm at the treatment of him and his family.
Mr Chen exposed how local authorities in Linyi, in Shandong
province, forced thousands of women to have abortions or be sterilised
as part of China's one-child policy.
US officials have often raised Mr Chen's case with China on human rights grounds.
Earlier, the EU urged China to "exercise utmost restraint" in
connection with Mr Chen, amid reports that some close to the activist
had been rounded up.
His colleagues said last Sunday's escape had taken months to
plan, and was carried out with the help of a network of friends and
activists.
He scaled the wall that the authorities had built around his
house, and was driven hundreds of miles to Beijing, where activists say
he stayed in safe houses before fleeing to the embassy.
Several people involved in Mr Chen's escape have been
detained or have disappeared in recent days, and fellow activist Hu Jia
has been questioned.
Source: BBC News