For a number of weeks, Wolves have been heavily linked with the Portugal international, who will be departing Estadio Jose Alvalade this summer.
With Wolves expected to receive funds from the sale of Ruben Neves at some stage, it has been recently suggested that the West Midlands outfit are the clear frontrunners to wrap up a deal.
However, according to Record, a transfer to Molineux is far from a formality with Fulham said to be ready to make their own approach.
Having secured promotion back to the Premier League, the Cottagers are looking to make an impact in the transfer market, their first piece of business allegedly being that of Lazio goalkeeper Thomas Strakosha.
While that deal would represent a coup in itself, winning the race to sign Palhinha would better that addition, the 26-year-old now a regular in the Portugal squad given his performances for Sporting over the past two seasons.
Although the report claims that Fulham are yet to make a formal proposal, it is claimed that they are willing to enter the race with a €20m (£17.01m) bid.
Given Wolves' status in the Premier League and an array of compatriots already being at the club, Palhinha may see his future under Bruno Lage rather than Marco Silva.
However, there is unlikely to be any movement from Wolves' end until they have receiving their desired asking price for Neves, something which appears unlikely in the short term.
Despite Barcelona being the frontrunners to eventually get a deal over the line, they currently do not have the finances to sign the 25-year-old for a fee in excess of £50m.
Furthermore, the Catalan giants are seemingly against including Nico Gonzalez in any proposal, the prospect allegedly being the only player that Wolves are prepared to consider in part-exchange.
On a positive note, the process could be fast-tracked if Barcelona are able to part ways with Frenkie de Jong, with Manchester United said to be willing to sign the Netherlands international for a fee totalling £68.5m.
According to a report, the La Liga side would receive £51m up-front, a fee which theoretically could tempt Wolves into pulling the trigger with the sale of Neves.