LA Galaxy head coach, Arena, is the favourite to replace Jurgen Klinsmann who was sacked on Monday.
Arena was the USA coach from 1998 to 2006 and led his country to two World Cups.
Grant is the other candidate after impressing
Grant led Ghana to the final of last year’s African Cup of Nations where they were beaten on penalties by Ivory Coast.
The former Portsmouth and West Ham United manager also led Chelsea to the final of the 2008 Champions League where they lost on penalties to Manchester United in Moscow.
Klinsmann was sacked as USA boss with his team bottom of their World Cup qualifying group following recent defeats to Mexico and Costa Rica.-skysports
The 52-year-old, who won the World Cup as a player with Germany in 1990, took over as US boss in 2011.
“We remain confident we have quality players to help us advance to Russia 2018,” said US Soccer president Sunil Gulati.
“But the form and growth of the team up to this point left us convinced that we need to go in a different direction.”
Klinsmann steered the United States to the last 16 at the 2014 World Cup in Brazil after finishing above Portugal in their group.
However, they lost 2-1 at home to Mexico and 4-0 away to Costa Rica in their opening two qualifying matches for the 2018 tournament.
The US are pointless and bottom of the six-country qualifying group, below the likes of Panama and Honduras, albeit only a fifth of the way through the qualifying process.
“With the next qualifying match in late March, we have several months to refocus,” added Gulati.
“We need to determine the best way forward to ensure a successful journey to qualify for our eighth consecutive World Cup.”
Former Tottenham striker Klinsmann was linked with the England job after Sam Allardyce left his post in September.