Chelsea's initial offer of €35m (£29.5m) for Jamie Gittens has been rejected by Borussia Dortmund, according to Sky in Germany.
Negotiations are ongoing between the parties and a new bid from Chelsea is expected.
Dortmund are understood to want €50-60m (£42-50m) for the forward.
The England U21 international wants to join the Blues and play for them in the Club World Cup, with a verbal agreement in place between the two.
Dortmund will also play in this summer's competition, with Chelsea having until Tuesday's deadline to get the deal done if they want Gittens to feature in the US.
The west London club are looking to strengthen in the winger position following the decision not to take up the option to sign Jadon Sancho permanently.
The 20-year-old winger was a target in January and despite losing his place in Dortmund's starting XI towards the end of the season, has remained high on a list of eight or nine attacking names Chelsea are working on this summer.
Chelsea may also sign another striker after already completing deal for Liam Delap, with Hugo Ekitike and Benjamin Sesko also on their shortlist.
But goalkeeper Kepa Arrizabalaga looks set to leave Stamford Bridge.
Arsenal are progressing with a deal to sign him and are expected to trigger the £5m release clause in his contract.
How Gittens can add spark to Chelsea attack
Sky Sports' Peter Smith:
It was not always thrill-a-minute under Enzo Maresca last season at Chelsea. Far from it. But Gittens can add spark to the team's attacking play.
Comparisons with Sancho are inevitable, given their career histories and preferred left-wing role but Gittens' output of dribbles and crosses at around twice the rate of the former Blues loanee illustrates the different approach the potential new arrival is likely to bring.
In fact, Gittens' mesmeric, high-speed dribbling ability is on another level in terms of frequency to what we have seen from Pedro Neto and Noni Madueke in the Premier League this past season, too. Gittens has been a livewire in the Bundesliga and the plan will be for him to translate that into Maresca's set-up.
On paper, it should be a good fit. As the passing network for Chelsea last season shows, Maresca likes his players to find the wingers high and wide. From there, Gittens will relish the one-on-one battles with full-backs as he looks to create opportunities to cut inside and shoot on his favoured right foot or go on the outside to cross for England youth-team pal Liam Delap or Nicolas Jackson.
Gittens' top speed of 35.96km/hr (22.34mph) was the 16th-fastest clocked in the German top flight last season and the prospect of him stretching defences or igniting counters is an enticing one for Blues fans who have found their side too predictable of late. If Sancho's lack of pace was a criticism aimed at him, it will not be an issue for Gittens.
Like most Chelsea signings, at 20 years old, Gittens has room to improve and experience to add to his game. He is not the finished article. But his unpredictability on the ball will be a welcome addition at Stamford Bridge if they can complete the deal.
'Gittens path to the top is a different one'
Sky Sports' Adam Bate:
When it comes to honing young English talent, Dortmund know how to do that better than most clubs in the Premier League. But Gittens' story is different to those of Sancho and Jude Bellingham who came before him before moving on for big money.
Bellingham arrived having had a season in the Championship with Birmingham City. Sancho ranked alongside Phil Foden as one of the jewels in the Manchester City academy. Gittens, signed at the age of just 16, did not come with quite the same guarantees.
A prospect at Reading, he had spent only two years at City, but was not close to the first team when Dortmund made their move.
"We do not want to find 30 players like other teams in England do it. We want to find the one player who can reach our first team," said Dortmund CEO Lars Ricken.
"When we signed him, he was not on Sancho's level but we said, we can develop him to the level of a great player. It was a good cooperation between our scouting department, professional department and youth department."
Chelsea value Maignan at £12.6m
Latest from Sky Sports News chief correspondent Kaveh Solhekol:
Chelsea have let it be known that they are prepared to pay AC Milan a maximum €15m (£12.6m) for Mike Maignan.
The Blues, who have not yet made a bid for the France goalkeeper, will not pay more than that for a player who will be 30 next month and has one year left on his contract.