Short answer: no.
Still, after the recent news about Cardinal Burke, some think so. But Fr. Dwight Longenecker offers some helpful context:
This Vatican re-shuffle had been on the cards for months. It may be part of a larger, intentional change of direction on the part of the pontiff, as Fr. Mark Drew observes in an excellent article here at the UK’s Catholic Herald, but set against this opinion is the fact that Cardinal Burke has just completed the usual five year term traditional for Prefects of the Apostolic Signatura. Those who shrug their shoulders at gossip about feuds say, “It’s no big deal. He was due for a transfer.” In answer to those who suggest that Burke’s transfer is a deliberate attempt on the part of Pope Francis to silence his enemies the shoulder shruggers would say, “Silence Burke? His new job as Patron of the Order of Malta gives him virtually no responsibilities, while providing him with a base in Rome and the time to travel, lecture, write and lead and make his point. Rather than silencing Cardinal Burke it could be that Pope Francis is giving him his voice and therefore encouraging the “loyal opposition” in a healthy way.A further argument against the “purge of conservatives” theory is that other noted conservatives have not been sidelined. Cardinal Pell is a prime example. A key member of Pope Francis’ consultatory group of eight cardinals, Pell was hand picked by Francis to bring about reforms at the Vatican Bank. Cardinal Mueller, head of the powerful Congregation of the Doctrine of the Faith, is another conservative voice close to Pope Francis. Both Mueller and Pell were also outspoken on behalf of the conservative faction at the synod. Those who suspect that a feud between Pope Francis and Cardinal Burke is part of a larger purge must acknowledge that the evidence is slim. It is true that Pope Francis is attempting to forward his agenda of change, but it is not true that he is kicking out everyone who disagrees with him.