The likes of Pogba, Eden Hazard and Kylian Mbappe have been heavily linked with Real as the Spanish giants look to regroup after a largely miserable campaign.
While Kroos admits he is a fan of Manchester United midfielder Pogba, he insists he is ready to take on all-comers in the battle for game time at the Bernabeu.
Speaking to the media after committing himself to Real until June 2023, the Germany international, when asked about Pogba, said: "We can talk about many names. I like this player but nothing changes for me.
"I will continue doing what I've done all these years, fighting for my place, playing well, and when I'm at a good level I think I have no problems."
Kroos was also quizzed about the possible signing of Pogba's World Cup-winning team-mate Mbappe.
Fresh speculation linking the quicksilver forward with Real has emerged in recent days but, with the 20-year-old costing Paris St Germain in excess of £125million, Kroos feels such transfer talk is above his pay grade.
He joked: "I like him as a player but this isn't a question for me. I cannot buy him. I have a good contract but I cannot buy him. It's a question for the club."
While the rumour mill is in full swing about potential summer arrivals at Madrid, there is also intense speculation about which players will be leaving.
Kroos was one of the players whose Bernabeu futures had been called into question but he insists he never saw himself leaving the club.
After signing a new contract, the 29-year-old now wants to help Zinedine Zidane's side bounce back from a forgettable 2018/19 campaign.
"It's a very happy and very special day for me," said Kroos. I've had a lot of success with Madrid, and I'm sure we'll have more in the coming years.
"I didn't think about leaving because I only thought about trying to change our situation. I want to leave when we're on top, when we're winning."
Although they won the FIFA Club World Cup again in December, Madrid saw their three-year reign as European champions ended by Ajax in the Round of 16, while also failing to last the distance in either LaLiga or Copa del Rey.
A lack of silverware only tells part of the story as a series of worrying performances resulted in Madrid finishing a mammoth 19 points behind champions Barcelona in LaLiga, sack two coaches and lead to speculation of a major summer overhaul.
Kroos concedes he does not know what the summer holds for the 13-time European champions but has assured supporters the team will do all they can to get back to the top.
However, he also warned that Madrid's remarkable recent success - Kroos has helped the club win 12 trophies, including three Champions League crowns, since joining from Bayern Munich in 2014 - should not be considered the natural order of things.
The 2014 world champion said: "The season has been disappointing, even more so when you're used to winning.
"But it's quite normal, this can happen. The thing that is not normal is what happened before. To win three successive (Champions League) finals is not normal. It seemed impossible and we did it.
"But we're already motivated for the coming season.
"We're going to try to get back to the high level of the other seasons. I'm not going to say that we will win everything but we're going to try."
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