The 31-year-old has scored eight times and registered one assist in 20 appearances for the Magpies during the 2023-24 campaign, including seven strikes in the Premier League.
According to the Daily Mail, Atletico approached Newcastle with a loan move for the experienced striker, but the Magpies were quick to turn down the offer.
The report claims that a permanent sale has not been ruled out, with Newcastle's difficulties surrounding Financial Fair Play leaving them in a vulnerable position.
Wilson, who is currently out with a calf issue, is believed to be open to a move to Wanda Metropolitano.
The experienced forward only has 18 months left to run on his contract at St James' Park and is allegedly likely to leave over the summer if he does not depart before the winter deadline.
Staying in the Premier League, West Ham United are reportedly exploring the possibility of signing Leeds United forward Wilfried Gnonto before the end of the January transfer window.
The 20-year-old handed in a transfer request at Elland Road last summer, but Leeds did not sanction his exit.
Gnonto has struggled to make his mark for the Championship outfit this season, only managing one goal and one assist in 23 appearances in all competitions.
According to Italian journalist Matteo Moretti, the attacker is attempting to force a move away from Leeds before the winter transfer window closes for business.
West Ham are allegedly the favourites for a player who has scored five goals and registered five assists in 51 appearances for his current side in all competitions.
Meanwhile, Sheffield United's hopes of signing Everton defender Mason Holgate on loan for the second half of the 2023-24 campaign have reportedly taken a major hit.
The 27-year-old is currently on loan at Southampton, making six appearances for the Saints this season.
According to PA, it had been agreed that Holgate's spell with the Championship outfit would come to an end to allow him to move on loan to Sheffield United for the rest of the season.
However, the report claims that the deal has now collapsed, as Sheffield United were told late in the negotiations that Everton would require a loan fee of £250,000.
The Blades had allegedly been willing to cover Holgate's wages but are not prepared to pay the fee.
The defender is said to have travelled to Sheffield United for a medical, and there is still a slight hope that a deal could be resurrected before the winter window closes for business.