Despite just one league win this term, the Scottish Premiership side are only two games away from the group stages of Europe's second competition.
Glentoran and Coleraine have already been beaten in qualifying, with Hapoel Beer Sheva up next week in Israel.
"You have to dream. Everything is a dream in football, said Gallagher.
"Probably a lot of people said last season that Motherwell getting to third place and into Europe was a dream. You have to keep dreaming. Without ambition, there's no point in football. We have to be ambitious, believe in ourselves to go over to Israel and get a result. We will be the underdog but hopefully that works in our favour."
Motherwell have had to do things the hard way to get this far in qualifying. While Glentoran were eventually battered 5-1 at Fir Park, it took the visitors going down to 10 men for the floodgates to open.