Former Bournemouth loanee Wilshere has been almost exclusively limited to Carabao Cup and Europa League duty by Arsene Wenger so far this season, making just two brief top-flight substitute cameos against Everton and Manchester City.
Such a lack of Premier League opportunities saw the 25-year-old omitted from England's initial squad for friendlies against Germany and Brazil, while he was further overlooked in favour of Jake Livermore and Jack Cork after Dele Alli, Jordan Henderson, Harry Winks and Fabian Delph were forced to withdraw through injury.
Gareth Southgate, who also attempted to call up Chelsea's Danny Drinkwater only to be informed that he was not fit enough to feature, has reiterated that Wilshere must be playing regularly in order to force his way back into the international fold, while also claiming that he is being deployed out of position at no.10 at club level.
With his England exile showing no signs of ending and Wenger's midfield pecking order well established, reports have suggested that Wilshere may have to leave Arsenal in January in order to keep alive his hopes of earning a place in England's squad for the 2018 World Cup in Russia.
West Ham United, Swansea City and La Liga outfit Real Betis are all said to be monitoring the player's situation, while The Telegraph recently claimed that struggling Palace were prepared to offer him a lifeline.
However, Hodgson has now firmly rebuffed that speculation, suggesting that it is merely agent-driven and that Wilshere, who is out of contract at the end of the season, had not been identified as a potential New Year transfer target during discussions with sporting director Dougie Freedman.
"It didn't come from us – we have never mentioned his name," he was quoted as saying by the Croydon Advertiser. "I work with Dougie Freedman and we talk about potential players. Jack Wilshere's name has never been mentioned.
"Now you are telling me we have been linked with him, but by who? I will tell you who, his agent, because that's where newspapers get their stories from."
Former Three Lions boss Hodgson is evidently a fan of Wilshere, having included him in his squad for Euro 2016 despite a similar lack of first-team football caused by a broken leg and an absence of full match fitness that became only too apparent during the course of the tournament. And while he admits he could be interested in his signature in the future, now is evidently not that time.
"We haven't discussed Jack Wilshere," he added. "I like him and I think he is a very good player. There may come a time at Crystal Palace where Jack Wilshere would be just the player we are looking for, but I can't tell you that is the case at the moment, and he might not be available etc, etc.
"So there's no point in talking about these things, but one day you might come with a name and say 'what about this fella', and that might to some extent have emanated from here, but Jack's name has definitely not.
"But good luck to Jack, I think he is an outstanding player and I have got nothing but respect for him, I like him very much, but why his name should be being talked about for Crystal Palace, I don't know."