A number of star names have departed Southampton since Pochettino left St Mary's Stadium to take the head coach role at Tottenham.
Luke Shaw moved to Manchester United, while Liverpool snapped up Adam Lallana and Rickie Lambert, with Dejan Lovren also in their sights.
Speculation has also gathered pace that Pochettino will return to his former stomping ground to lure France international midfielder Schneiderlin to White Hart Lane.
Pochettino is looking to add further reinforcements to his first-team squad following the arrivals of full-back Ben Davies and goalkeeper Michel Vorm from Swansea City, but he kept his counsel when questioned about Schneiderlin.
"We're trying to improve the squad but I never speak about players from other clubs," he said. "I have respect. I'm just focused on my team."
Pochettino was speaking after Tottenham defeated Chicago Fire 2-0 on Saturday, as the club ended their pre-season tour of the United States unbeaten.
And the Argentine was happy with the progress his side made during their visit to America.
"I'm very pleased for the players because we've finished with a good win, a clean sheet and that's a boost for the confidence," he added.
"It was difficult in the humidity but well done to the players, it was a good game out there. I'm happy for all of them. I thought we played well.
"We've worked hard on this tour and congratulations to the players, staff and the supporters, they've been fantastic."