The head coach confirmed that he has had no contact with the former Leeds United striker.
Evans described talk of an approach for Becchio as “news to me” after Becchio’s appearance in Leeds over the weekend sparked speculation about the 31-year-old rejoining the Whites.
Becchio is out of contract and available on a free transfer after injury forced him to cut short his contract at Argentine club Belgrano in September.
The forward, who joined Belgrano from Norwich City during the summer, agreed to terminate his deal due to an ankle injury which would have ruled him out of the whole of Argentina’s domestic campaign.
Becchio is held in high regard by both Leeds and Evans having shone in four-and-a-half years at Elland Road and played under Evans while on loan at Rotherham United last season.
Evans, who declined an opportunity to take Becchio to Rotherham permanently before the forward’s switch to Belgrano, is looking to add a new striker to United’s squad but Becchio is short of full fitness and has not started a competitive game since September 2014.
United’s head coach told the YEP: “I’ve had no contact with Luciano so the rumours about him are news to me.
“I had a great relationship with him at Rotherham and he’s a terrific lad but I’ve not spoken to him for about 12 months now. If he’s in Leeds, whatever the reason, I’d be very happy to catch up with him for a coffee but only for a coffee.
“He was very good for us at Rotherham but it took us six or seven weeks to get him properly match fit in the first place. After that he started to look like the player we knew he was. With where we (Leeds) are at just now, we’re looking at players who can come in and make a difference immediately.”
Becchio produced 86 goals during his spell with Leeds, establishing himself as 10th in the list of all-time league goalscorers at Elland Road.
United caused controversy in January 2013 by allowing him to join Norwich as part of a £2m swap deal which saw Leeds sign Steve Morison and take a fee of £200,000.
Owner Massimo Cellino has turned down previous chances to recruit Becchio, including one last January when the striker was recommended as a target by ex-head coach Neil Redfearn.
Evans is hunting for new players and is looking to sign a goalkeeper on loan with the position of first-choice Marco Silvestri under threat after a series of mistakes this season.
United, however, are also expected to bring an additional forward to Elland Road before the Football League’s emergency window closes towards the end of next month.
The club showed an interest in Norwich City’s Kyle Lafferty earlier this season and could renew their interest in the Northern Ireland international with Evans’ squad 17th in the Championship and currently averaging less than a goal a game.