Media reports have incorrectly suggested the Italian could look for a move as soon as January having struggled to settle into life on the south coast.
Pochettino insists that is nonsense and is confident the striker will adapt to life in the top flight.
He said: “Nowadays with social media like Facebook and Twitter anybody can put any type of news out there and so we don’t really pay attention to that. We take those things for what they are and focus on the reality.
“The toughest thing is that on social media you can’t prove anything or disprove anything.
“Anyone can throw any kind of news out there and it’s hard to disprove or prove that news.
“For us the most important thing is that we know the personal situation of every single player and we just have to keep going and not pay attention to that.”
He added: “He’s still in the process of adapting.
“There’s a big difference between the Spanish, Italian and the Premier League.
“After getting to know the French league, the Italian league and the Spanish league I think being here in England this is the toughest competition.
“It’s the most competitive and especially for strikers the period of adapting to this league is quite difficult for them so I think he is still in the process of adapting.
“Every player needs their own personal time to adapt to this league.“Every player is different but I am sure he won’t have any problems adapting to this league and I’m sure that in a few months we are going to see the best of him.”
Osvlado is set to return to the Saints squad to face Stoke at the Britannia Stadium tomorrow along with Steven Davis.
The pair were forced to sit out last weekend’s win over Fulham but are fit again, leaving Pochettino with the decision as to whether to recall either one or both of them or stick with a winning side.
“It’s a good problem to have,” he reflected.
“It makes me very happy that both Osvaldo and Davis can return to the starting team and in the game against Fulham we played as a team and got the win and that’s the most important factor.
“It just shows me that the 23-24 players that I have available can all do well for this team and then it’s down to me as the manager to make the decision as to what players will be playing.”