Los Angeles Galaxy were keen on Frank Lampard before he signed for New York City, with the Californian club eventually recruiting Steven Gerrard.
Lampard and Gerrard have been compared throughout their careers with the two English internationals playing similar roles for the clubs where they built their impressive reputations - Chelsea and Liverpool, respectively.
"We recruited Frank pretty hard here," Arena told the Mirror.
"The deal was close."
The 63-year-old coach added: "We talk to pretty much every single player that is interested in coming to the US and certainly when you hear Frank Lampard is willing, you're gonna have a lengthy conversation.
"I got to know Frank and visited him in London and he's a fabulous person and player and he's really going to help football here in America. He's going to do really well."
Lampard was reported to have signed a contract with New York City in July 2014 but spent the entire 2014-15 season with parent club Manchester City - who eventually claimed the midfielder had only made a non-binding "commitment" to MLS.
Lampard leaves the Premier League with 609 appearances to his name and 177 goals, while Gerrard, 35, hit the back of the net 120 times in 504 league matches for Liverpool.
