The Dutchman spent the first half of last season on loan at Tottenham Hotspur, before spending the second half of the campaign with Everton.
Danjuma has since returned to Villarreal and has made a positive impression in the club's first two matches, scoring against Atletico Madrid and Sevilla.
While the 27-year-old has started the first two La Liga games, there is still some uncertainty about whether he will still be at the club beyond the summer transfer deadline.
According to Football Insider, Forest are preparing to launch a potential move for Danjuma in the latter stages of the transfer window.
Forest are currently focused on sealing a deal for Arsenal's Eddie Nketiah, but they could turn their attention to Danjuma once they have signed the one-time England international.
Danjuma is believed to be looking for a permanent transfer rather than another loan move as he looks to find stability in his career.
Celtic make contact over Bogusz move
Meanwhile, Scottish Premiership champions Celtic are reportedly interested in signing Mateusz Bogusz from Los Angeles FC.
Celtic are set to bid farewell to Matt O'Riley after reaching an agreement to sell the midfielder to Brighton & Hove Albion.
As a result, the Hoops are set to lose the services of a player who scored 19 goals and provided 18 assists in 18 assists in 49 appearances last season.
With O'Riley heading towards the exit door, Football Insider are reporting that Celtic are looking to strengthen their squad with the addition of LAFC's Bogusz.
The report claims that Celtic have made an enquiry over Bogusz, but any move for the attacker will be dependent on O'Riley's potential exit.
Bogusz has scored 21 goals and contributed 14 assists in 75 competitive appearances since joining LAFC from Leeds United in March 2023.
Aberdeen sign Nisbet on loan
Staying in Scotland, Aberdeen have confirmed the loan signing of Millwall striker Kevin Nisbet.
The striker scored 39 goals in 101 Hibernian appearances before he completed a £2m move to Millwall last summer.
Nisbet had to settle for 17 starts in 27 Championship matches last season and made a brief substitute appearance in Millwall's first match of the 2024-25 campaign.
Having failed to establish himself as a regular starter in the English capital, Nisbet has returned to Scotland to join Aberdeen on a season-long loan move.
The 27-year-old told the club's official website: "As soon as I knew Aberdeen were interested, it was a no brainer to be honest. I did have options down south and with other teams in Scotland but the way the team have started the season, I wanted to get involved.
"This is a massive club. It's one that makes an impression on you and I want to be part of that. I spoke to the gaffer and listened to his philosophy and his plans.
"I was impressed with his style of play and I believe it suits me. It is an exciting project that I want to be part of and I am ready to give it my all for the fans."
Nisbet will be part of Jimmy Thelin's side for Sunday's Scottish Premiership home game against Kilmarnock.