Manchester City have tabled a second bid of around £40m for Liverpool and England forward Raheem Sterling, according to Sky sources.
Sky reported on Tuesday that Chelsea were interested in signing the 20-year-old but were not prepared to meet Liverpool's £50m valuation for the player.
With the winger refusing to sign a contract extension at Anfield, a number of Europe’s clubs have been linked with a move, but it would seem only City have made any official bid.
It is understood City had a £25m-plus bid rejected last week and Sky sources are reporting on Wednesday that last season's Premier League runners-up have returned having improved their initial offer by a figure in the region of £10-15m.
Sterling joined Liverpool from QPR in 2010 and is under contract until 2017, but has turned down the offer of a new deal worth £100,000 a week.
Liverpool manager Brendan Rodgers insisted last month he expected Sterling to stay for the remainder of his current deal.
City chairman Khaldoon Al Mubarak revealed last week how his club were planning to heavily invest in new players this summer.
"You will see us in the market bringing in high-quality individuals that fit within what we are aspiring to," he said.
"We want a squad which is able and has the capability and quality to win the Premier League, to compete and win the Champions League and be able to go all the way in two cup competitions in England."
Sterling has maintained throughout negotiations that his issue is not about money, stating in April not sanctioned by the club that he did not want to be viewed as a "money-grabbing 20-year-old".
Liverpool's sixth-place finish means they cannot offer him Champions League football next season and a disjointed campaign on the pitch personally has not helped.
The forward enjoyed his best form as a left-sided attacker alongside Luis Suarez and Daniel Sturridge the season before last in the Merseysiders' title near-miss but in the last 12 months he has found himself shunted between right wing-back, right wing, a number 10 and a central striker.
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