The Saints boss was quizzed at length this afternoon on the subject, following the 28-year-old forward's alleged headbutt on teammate José Fonte in training last week.
Pochettino side-stepped most of the questions fired his way, but did say he must move on from the incident and look at what is best for the squad.
“This is something that is in the past,” he said. “We like to see the future.
“What is done is done, and now we are fully focused on concentrating on what is better for the team in the future.”
Pochettino added: “It is clear it is not a nice situation, but not only here, it happens everywhere in the world.
“But, as a manager, I have to look for what is better for our club, to look forward to the future.”
Asked if it would be better for the club to be without Osvaldo past the end of the week, when the transfer deadline passes, Pochettino said: “We don’t know.”
However, should the Italian international depart St Mary’s, Pochettino hinted a replacement could possibly be brought in, with the manager saying the club were “working on certain aspects” in the window.
“Of course, we are prepared for everything,” he said. “We have got a great group of scouts working on it, and we are prepared for anything that can happen.”