La Viola agreed a deal to bring the prolific striker to Stadio Artemio Franchi on Monday, with the fee believed to be in the region of 16 million euros.
Gomez is expected to undergo a medical and agree personal terms before being unveiled as a Fiorentina player on Thursday, and Montella believes supporters can expect big things from the 28-year-old.
"It's only right that they dream," the ex-Italy international told reporters. "We know that it's going to be hard, but it's right that the fans dream because if you can't dream, then there's not much left. Certainly only what happens on the field will show whether this side are capable of repeating what we achieved last season, and then we can look further.
"Everybody knows he's a great player and that we're delighted to get him. We hope to impress again, both in terms of results and the way we play. That is what I hope for."
It is anticipated that Gomez will link up with Giuseppe Rossi in attack, although there has been speculation that Fiorentina will sign another forward if Stevan Jovetic is sold.
Montella, though, is refusing to be drawn on the speculation linking the Viola with acquiring yet another attacker.
"We'll have to see," the former Roma ace added. "You can always improve your squad so I always expect the best and the most.
"But let's take things one step at a time for now. The first step should be the official announcement of Gomez."
The Germany international scored 75 goals in 115 Bundesliga appearances for die Roten.