But there are also plenty of big names who are seemingly unhappy with their current situation and could be on the move.
Here, Standard Sport takes a look at ten of them…
Hooked at half-time of Tottenham's opening day defeat to Everton, Dele has barely had a sniff in the Premier League since. Even with a nine-man bench, he was absent from Jose Mourinho's match-day squad against Leicester. Paris Saint-Germain are among the top European sides interested in a loan for the 24-year-old next month, while Spurs may consider sanctioning a permanent deal. Dele is desperate for regular football as his European Championship dream slips away.
The defender has arguably been hit the hardest of any of Chelsea’s next generation by their spending in the summer. It is hard to see Tomori get too many chances in the second half of the season, with Frank Lampard blessed with options in central defence. Leeds have been linked with a January move for him and it may be best for his development to get some regular first team football in the Premier League.
The Dane's search for a fresh challenge in Italy has not gone to plan. After an unhappy lockdown, spent largely alone in a new country, Eriksen has found himself as a bit-part player for Antonio Conte's Inter Milan. A return to the Premier League must be appealing but former club Tottenham appear to have moved on, with Harry Kane now pulling the strings at No10 and Tanguy Ndombele and Giovani Lo Celso finding their feet. Manchester United or even Arsenal offer a more realistic escape route if Eriksen wants a return to more familiar challenges.
The German will have six months to run on his current contract in January and, while he is most likely to leave when that expires in the summer, he could depart mid-season. In the summer, the only real interest in Ozil came from clubs in Qatar and Saudi Arabia - but MLS and Turkish sides are monitoring him too now.
The Arsenal left-back was very close to joining Bayer Leverkusen in the summer but the deal fell through late on. A move back to Germany looks on the cards again, though, for the Bosnian with a loan deal seemingly likely. Arsenal are happy to let him go to get his £100,000-a-week wages off their books.
The France striker has well and truly put himself in the shop window as 2020 nears a close – and his motivation remains next summer’s Euros. There will be no shortage of suitors if he agitates to leave Chelsea, so the question is whether Frank Lampard can convince him he will get enough game time at Stamford Bridge. With so many games and trophies to play for this season, the promise of silverware with Chelsea, rather than France, could ultimately determine if he stays put.
The French defender is still yet to make his debut for Arsenal and is expected to leave on loan during January. He very nearly left for his old club Saint-Etienne in the summer, but a deal collapsed at the last minute. They are the frontrunners to tie up a loan deal for the rest of the season. The defender is still yet to make his debut for Arsenal and is expected to leave the club on loan during the January transfer window. He very nearly left for his old club Saint-Etienne in the summer, but a deal collapsed at the last minute. They are the frontrunners to tie up a loan deal for the rest of the season.
The Spaniard simply has to leave Chelsea. Having the world’s most expensive goalkeeper sitting on the bench isn’t a good look for anyone. His time at Stamford Bridge looked numbered long before Edouard Mendy’s arrival, but the Senegal keeper’s form since signing from Rennes has only confirmed the club’s need for a reliable No1. It hasn’t worked for Kapa in England and a fresh start is needed.
Crystal Palace are well stocked at centre-back, and are keen to significantly lower the age of their back line. Former Liverpool defender Sakho is out of contract in the summer and has not played since coming off the bench at Fulham in October. Should anyone come knocking it would make good sense for Palace to try and squeeze some money out of one of their top earners before he becomes available on a free in six months’ time.
The Burnley defender missed out on a move to one of West Ham or Leicester during the summer and is in no rush to sign a new deal at Turf Moor. Brendan Rodgers moved for Wesley Fofana while David Moyes in unlikely to have the funds to afford Tarkowski next month. But with his contract running down Burnley’s asking price will have to fall, and he wants to leave to boost his chances of a place in the England squad for the Euros.