I believe they can do that with the current squad. Although most people would not be very supportive of Barcelona. I see there are a lot of opportunities at the moment, when Atletico Madrid and Real Sociedad are at a disadvantage. Barcelona only need to win from Mallorca later on January 1 next. About 2 points is enough to raise points to rank 5 or 6.
Barcelona just need to maintain the consistency of their game in every match to win. It may sound difficult for Barcelona to play against big team like Sevilla, Atletico Madrid and Real Madrid, but the good thing about them now is that there is an improvement in the performance of their players. Barcelona are a big team in Laliga and I think they know what to do to improve their form, so I don't think qualifying for the Champions League next season is impossible.
I will probably look forward to the Mallorca vs Barcelona game in January, I think they deserve the 3 points there. Maybe Alves can also be listed as a regular player in January and also some new players who have arrived in the transfer market. That will help Barcelona improve its performance.