The world No1 is set to play at the Aspall Tennis Classic exhibition event at the Hurlingham Club this week in order to ensure sufficient match-time on grass before beginning his Wimbledon defence next week.
Zverev is also looking to become the only player this year to win titles on hard, clay and grass courts while the Swiss is targeting his ninth title here at the Halle Open.
Federer, whose first success at Halle came in 2003, has won 92 career titles from 140 finals.
The Swiss lured the youngster to the net on several occasions, including at 4-4 in the second set when the Russian dumped a forehand volley into the net to give Federer two break points.
Zverev booked his second successive final spot when he beat Frenchman Gasquet 4-6 6-4 6-3.
GETTYRoger Federer admits he is on cloud nine with his game at the moment
Federer - who lost to Tommy Haas at the Stuttgart Open last week as he returned to action following a two-month break - coasted through the opening set.
"It's great to get off to a good start in the finals and then remind yourself that you've been playing good tennis all week", said Federer after improving to 4-0 in title matches this year, tied with Rafael Nadal for the tour lead.
Germany's Zverev, 20, beat Federer in last year's semi-final, but could not match the 18-time Grand Slam champion.
After enjoying good weather all week, the rain finally made an impact on semi-finals day at the Aegon Championships at Queen's, where Marin Cilic and Feliciano Lopez will contest Sunday's final.
"People in their thirties, maybe 31, 32 when traditionally we're thinking "well, he's going to start wrapping it up soon" and think well maybe I've got four, five years". At 35, the Swiss player became the oldest victor of the grass-court tournament.
This is going to be a fun match between these two talented players, as Zverev is growing up before our eyes and Federer is, well, Federer.
Iran's policy is to strengthen ties with Qatar, Rouhani says
In his letter , Corker said he was pleased with President Donald Trump's trip to Saudi Arabia, which included a summit of the GCC. They accused Qatar of "sponsoring terrorism", allying with Iran, and hosting "fugitives" wanted by Saudi Arabia or its allies.