Wales host the  showpiece event on Saturday, 3 June, at the Principality Stadium in Cardiff.
Speaking to BBC Wales, chief executive Jonathan Ford said he "would love the FAW to be considered in the future to host these major events".
He also said Wales' run to the semi-finals of Euro 2016 has boosted their standing in the game.
Hundreds of millions of people around the world are expected to tune in to watch the Champions League final live.
Ford said the FAW had built up its credentials in hosting major tournaments and matches, and he wanted more.
"We do not want it to just stop there in June," he explained. "We would like to continue to do it."
Wales has already hosted the Uefa under-19s Women's championship in 2013 and the Super Cup final in 2014, but the Champions League final is a giant step up, with estimates it will generate £45m for the local economy.
"We are at the business end now," Mr Ford said.
"We have got a team of 12 people at the FAW working full time on it, and in Wales alone there are probably several hundred people working on it.
"That will go up when Uefa are over here and if you add in the volunteers and the people working in the stadium then you are probably talking about four to five thousand people who will work this event.
"There is a lot of work being done to make sure this is successful and to make sure we utilise it to achieve the objectives we have with football."
Hundreds of thousands of spectators - with and without tickets -  are expected to travel to south Wales in the days leading up to the final, with the FAW, police, governments and local authorities involved in a huge logistics exercise.
Details of road closures and restrictions in the Welsh capital are yet to be officially published, but significant disruption is expected.
Major sporting events in the Welsh capital have been dogged by transport problems in the past, down in part to capacity issues at Cardiff Central railway station and pinch-points on the M4 at the Second Severn Crossing and Brynglas Tunnels in Newport.
BBC Wales has been told that 10% of the UK's entire rolling stock of coaches will be used to bring fans in and out of Cardiff on the day of the final and 21 intercity trains will be in place after the match to take supporters from Cardiff back to London.
Wales take on Ireland in a World Cup qualifier on Friday, still unbeaten in their group, but needing a win to improve their chances of qualifying for the finals in Russia next year.

French just edged into the top eight in the individual event for a place in Rio, with Samantha Murray 10th and Freyja Prentice 13th.
Their combined scores helped them finish ahead of Italy and Germany.
Olympic champion Laura Asadauskaite claimed the women's European gold.
Asadauskaite, who started the run-shoot a combined 59 seconds behind eventual silver medallist Elodie Clouvel of France, had already secured her place in Rio by winning the World Cup final in June.
It meant ninth-placed Alice Sotero of Italy was also rewarded with an Olympic berth in a race which saw Germany's Lena Schoneborn take bronze at the University of Bath.
French was delighted by her career-best result which secured Britain their third Olympic place - following  Joe Choong's seventh place in the men's event on Saturday and Murray's fifth at the 2015 World Championships.
"It's amazing, I never thought I would be able to do it," French told BBC Sport.
"I thought I was pretty average all day to be honest, but held it together in the run-shoot at the end and now I just have to stay strong next year."
Murray - the silver medallist at London 2012 and 2014 World champion - was expected to challenge for her first European title.
She ranked second after the swimming and fourth after the fencing stages, but dropped to ninth after the showjumping round and struggling with her shooting in the final event.
"There was a lot of pressure," Murray admitted to BBC Sport.
"I've had a difficult year with some injuries and some personal things going on so hopefully next season will be a fresh start. I'm looking forward to a clean slate."
World junior champion and 2014 Youth Olympic silver medallist Francesca Summers finished 29th in her senior international debut.
The Football Association of Wales is considering a future bid to host another Champions League final.
[NEXT_CONCEPT]
British pentathletes claimed women's team gold as Kate French secured Olympic qualification on the final day of the European Championships in Bath.