Spurs have been linked with the Burnley defender and the Bayern Munich winger this week, as the summer transfer window draws closer.
It is believed that Pochettino is already making transfer plans at Spurs, with a number of players on his sights.
But the Argentine boss refused to confirm whether he did have interest in bringing either Keane or Costa in.
“Many rumours, eh? I cannot speak about rumours,” Pochettino said.
“If we focus on one rumour, maybe we need to speak about not players but myself and different things. Today we must be focused on Saturday and the end of the season, and all that happens about players in, players out, you will know when we finish the season.”
Both Keane and Costa would be exciting signings for Spurs, as they look to add depth to their squad next season.
Keane has been rock solid for Burnley this term, and has earned an England call-up after a series of good performances.
Costa, meanwhile, has been used a rotational option by Bayern this term - but his quality is undoubted.
The Brazilian is regarded as one of the top wingers in world football, and his arrival would give Tottenham one of the most feared frontlines in the Premier League.