The governing body says the Turkish bid is the main rival to Wembley to stage the fixtures after 32 Uefa members expressed an interest in hosting games.
"We've taken some soundings. There's a sympathy for Turkey and it does feel like they are the front-runners," said the FA's general secretary Alex Horne.

Uefa, the European football governing body, decided the tournament would not be staged in a single country but instead shared between 13 cities across Europe."We get the politics around Istanbul, having not got the Olympics."
The decision to give Tokyo the 2020 Olympics may now clear the way for the city to host the finale of Euro 2020 given that Uefa's president, Michel Platini, is thought to retain his long-term support for the Turkish FA's ambitions.
Uefa is offering member countries the chance to bid for two packages of matches encompassing either group stage games and a knockout round match or the semi-finals and final.
The FA will now bid for both packages as will, BBC Sport understands, Belgium, Spain, Germany and Wales.
Turkey and Ukraine are believed to have bid only for the semi-finals and final, leaving 25 other nations, including Scotland, bidding solely for group stage and knock-out fixtures.
Horne, speaking as the FA announced its financial results for 2012, believes Wembley and London would benefit from the award of either option.
"The impact on the stadium and London of hosting either group stages and semi-final and final will be significant. It's something we want to be part of. So we've bid for both."
FA chairman Greg Dyke has targeted a semi-final place for England at the 2020 tournament and Horne believes hosting games would provide a boost should England qualify.
"The prize of group games and a quarter-final, or certainly a knock-out game, here at Wembley, is significant.
"You get two games with England at home which has got to be an advantage."
The FA's financial results reveal that turnover for the not-for-profit organisation in 2012 stood at £318m, down from £329m in 2011. Over 50% of total expenditure went towards investments in the national game, with £101m given in total, including £43m given directly to grassroots football projects.
Fabio Capello's departure as England manager in February 2012 is also accounted for in the financial statement. After Capello and his back-room staff left the England set-up the team remained without a manager until current boss Roy Hodgson was appointed shortly before Euro 2012.
While the terms of Capello's financial settlement remain confidential, Horne made clear that the Italian's departure had been managed: "We didn't pay Fabio any more than we would have done in the period that we didn't have a manager," he said.
"We paid him a small amount of money as severance but it was less than we'd have paid him if he stayed working until the Euros, significantly."
The £11m decrease in turnover, when compared to 2011, is largely due to Wembley Stadium, which is wholly owned by The FA, suffering a fall in event income.
The FA say this was due to a lower number of events held in 2012 when compared with 2011 when the stadium staged the Champions League final between Manchester United and Barcelona.
The London 2012 Olympics also meant the Community Shield had to be played at Villa Park.