The 26-year-old Portuguese shot-stopper joined Cluj last summer when they paid Braga just £400,000 for his signature.
However, Felgueiras has excelled for Cluj, producing some top displays in the UEFA Champions League.
And it is claimed that Manchester United manager Sir Alex Ferguson was personally impressed with Felgueiras during both of their games against Cluj in the group stages.
Everton were previously linked with the player, who admitted he was flattered by the interest.
Now Cluj president Iuliu Muresan admits he could be ready to sell Felgueiras, but only if they receive more than €4.5million, which would represent a club record.
"Felgueiras is the most transferable player right now in our group," Muresan told Digisport TV.
"We had problems with the goalkeepers in the previous years, but Mario has brought a great stability in our defence.
"We don't want him to leave this winter, but an offer of at least 5million would change the situation - basically, Felgueiras will be our richest ever transfer."