Disney shares were on the rise to kick off 2020 after some Wall Street analysts estimated significant growth from its new streaming service and recommended clients keep buying the stock.

Disney+ will attract 25 million users by the end of the first quarter, Rosenblatt Securities analyst Bernie McTernan said in a note Wednesday, citing his firm's survey of video users. He previously estimated that figure to be 21 million subscribers.

"Awareness of the service and penetration of respondents has continued to trend higher throughout our surveys," he said.

McTernan reiterated a $175 price target and a buy rating on Disney, and added that the growth of Disney+ may be pulling some users away from Netflix.

Disney stock closed up 2.5% Thursday at $148.20 a share. The stock jumped more than 31% in 2019.

"For Disney+ subscribers, 29% indicated they unsubscribed from another streaming service as a result of subscribing to Disney+, and 9% specifically indicating they unsubscribed to Netflix," McTernan said.

Disney has not disclosed subscriber numbers since the launch of Disney+ in November when the company said it signed up a whopping 10 million subscribers in one day. Disney has said it will not disclose new numbers until its quarterly report in February. Last month, however, independent app-tracking company Apptopia reported Disney+ mobile downloads of 22 million and said the app has averaged 9.5 million daily active mobile users, ranking in the top spot in Apple and Google's app stores.