The 20-year-old midfielder left the Sky Blues for Newcastle United in the summer of 2012.
He continues to be handled with care by the Magpies, with just one Capital One Cup outing made this season.
A lack of action has sparked speculation that he could be allowed to head elsewhere in order to get regular playing time.
Coventry were reported to be keen on welcoming the England U20 international back into their ranks, but Pressley insists that is not an option he has been exploring.
He said in the Coventry Telegraph: "There's no truth in that. He's obviously a very talented player.
"But he's not somebody we are looking at."
While Bigirimana's patience may be tested further over the coming months, he has expressed a desire to remain on Tyneside and fight for a place in Alan Pardew's plans.
He said in the Evening Chronicle: "I'm going to stay here. I'm going to be patient, and I'm going to work my socks off.
"I showed last year that I didn't look out of place in the big games. That's not being big-headed, that's how I feel I did.
"So I'm not going on loan. My target this season is to fight. You never know how the season can change.
"Patience is the key. In football, you've got to be patient. You've got to stay fit and keep working in training."