Stoke City are currently five points behind Manchester United, who are in fifth place.
The Potters' next two league matches are at home against relegation threatened Aston Villa and Newcastle United, and Shaqiri believes if his side can pick up maximum points in those games they will be able to push on.
“Every team wants to play in the Champions League or Europa League,” Shaqiri said.
“Look at Leicester for what is possible. Last season they were fighting relegation, this season they are top, so anything can happen in the Premier League.
“We are five points behind United with two home games coming up against Aston Villa and Newcastle — if we did get six points we can look again.
“At Bournemouth getting the first goal was important after not scoring as a team for so long. You could see we relaxed a bit after that and played better.
“It was a day when we showed the quality we have.”
Stoke won their last match against Bournemouth 3-1, to end a winless run of three games.
The Potters have had a rather up and down season so far, but there is no doubting the progress that they have made under Hughes’ stewardship.
At the moment, Stoke sit five points behind United, who are in fifth place, leaving them with some work to do to meet Shaqiri’s ambitious target.
The Potters do not have any added distractions as they chase down a European place, however, as they are out of both the FA Cup and the Capital One Cup, and that could work in their favour as the season reaches its climax.