European and Asian investments are moving fast into Iran, leaving the U.S. in the dust as some sanctions continue to keep American money out despite keen interest, an investor said Thursday.

Broad western sanctions against Iran were lifted in January this year after the government agreed to curb its nuclear program, spurring investment into the country with Airbus announcing a large $25 billion order of 118 airplanes while automaker Peugeot returned to the country with a 400 million euro ($435 million) deal.

Japan and Singapore have also signed bilateral trade deals with Iran recently.

The U.S. however is "nowhere in terms of trade" due to remaining sanctions over Iran's human rights policies and concerns about terrorism, David Grayson, chief executive of New York-based brokerage Auerbach Grayson told CNBC's "The Rundown" on Thursday.

"Basically, the Iranians can sell carpets, rugs and caviar to the U.S. but beyond that, the U.S. is being left at the station and the train is pulling out," Grayson said.

Grayson said he has received interest from American clients to invest in the Tehran Stock Exchange but sanctions aside, there is no recognized custodial service to hold securities on behalf of international investors yet.

Iran offers potential to investors despite recent economic wobbles and a far from clement political backdrop in the region. The country has a population of 80 million with a median age of approximately 29 years and a tertiary education enrollmentrate that is higher than many developing economies.

The exchange has a market capitalization of $100 billion and processes $100 million worth of trades daily, according to Grayson, who visited Iran as a tourist last May.

Gains by reformist candidates in last weekend's Iranian elections may pave the way for changes to economic policies that will boost foreign investment and trade with the west, but there will still likely not be action from the world's largest economy for months until the new president takes office after the election in November, said Grayson.

This article was written by Huileng Tan for CNBC on March 3, 2016.