The former Tottenham boss, 69, has agreed to oversee upcoming World Cup qualifiers against Bangladesh and Australia.
Jordan must win them both to reach the third round of Asian qualifying for the 2018 finals in Russia.
"If we win them and everyone is happy I'd love to come back," said Redknapp.
"We have to make sure we win. At the moment it's two games but we'll look to the future after these two games. There's nothing I would like more than to be successful in these games."
Jordan, who have never qualified for a World Cup, are second in their group in the second of three phases of Asian qualifying.
Redknapp, who has also taken up an advisory role at Championship side Derby County, was approached by Jordan Football Association president Prince Ali bin Al Hussein earlier this month about taking charge of the side ranked 82nd in the world.
It is Redknapp's first managerial position since leaving Queens Park Rangers in January 2015.
"He is a world-class manager and he has proven that throughout his career," said former Fifa presidential hopeful Prince Ali.
"It is very rare you have people of this class. I spoke to many people but immediately it became evident Harry is the man for the job."
Harry Redknapp is open to the possibility of extending his spell in charge of Jordan beyond an initial two-game deal.