After impressing during his two years at Elland Road, the winger is being allowed to leave this summer with Leeds undergoing a rebuild under Jesse Marsch.
Such is the level of the overhaul that Marsch has already made five new signings, and a sixth is expected to follow in the form of Luis Sinisterra.
The Feyenoord attacker is regarded as a like-for-like replacement for Raphinha, increasing the desire for Leeds to finalise the Brazilian's exit.
However, while there are clubs who are willing to pay Leeds' valuation for the 25-year-old, Barcelona are yet to meet the criteria demanded by the Premier League side.
According to Sport, Leeds officials have now told their Barcelona counterparts to improve their proposal so that a deal can be completed.
Although Chelsea have already met Leeds' asking price, the player is said to prefer a switch to Camp Nou and is ready to remain patient to achieve what is described as "a boyhood dream".
Nevertheless, that is not something which suits Leeds, who want to press on with their own transfer business after narrowly avoiding relegation to the Championship in May.
Previously, it has been claimed that Barcelona's offer came with numerous instalments, whereas Leeds want to recoup as much of the transfer fee in one sum.
Barcelona president Joan Laporta has already acknowledged that the La Liga outfit are attempting to negotiate a deal with Leeds.
Speaking earlier this month, Laporta said: "We have spoken to Leeds and I don't think they will be offended. We have communication. What happens is that there are other clubs who want Raphinha and they are making their proposals."
Raphinha's agent Deco - who represented both Barcelona and Chelsea during his playing career - has previously been seen at the offices of the former as he continues to negotiate terms.
Chelsea are on the brink of wrapping up the transfer of Manchester City winger Raheem Sterling in a deal which is expected to be in excess of £45m.
However, their acquisition of the England international is not expected to prevent head coach Thomas Tuchel when it comes to signing another star name for the final third.