Spanish investment company Thesan took over the team from previous owner Jose Ramon Carabante in July of last year.
Since then the team has moved to a new factory in Madrid, where the Spanish squad has started working from this season.
HRT has been at the back of the grid this year and is currently in last place in the standings.
AUTOSPORT understands the team came close to a sale to a Middle East-based buyer at the end of last month, and that talks are still ongoing.
Thesan said in a statement on Monday that it was time for the team to find a new owner that would help it move forward.
"The current owners of HRT Formula 1 Team, TC II S.a.rl., would like to confirm that they are currently in talks with a number of groups interested in buying the team," said a statement issued by the team.
"HRT Formula 1 Team's current management hopes to conclude the sale in the upcoming weeks and, with it, enable the team to continue progressing and become a reference in modern-day Formula 1 after the important achievements already accomplished in this 2012 season.
"HRT Formula 1 Team hopes to communicate the name of its new owner in the upcoming weeks.
"We believe the moment to let new investors come through for HRT Formula 1 Team has arrived.
"We're very proud of the work done by the entire team and of the excellent sporting evolution achieved but the time has come for the team to continue growing with new financial backing.
"We're convinced that the sporting potential of the team is huge and that the presence of new investors can give it a big boost."