The 29-year-old Argentinian has been identified as a player to enhance the Canaries' forward options.
Following the 1-1 draw with Tottenham which extended Norwich's winless run in the Barclays Premier League to seven matches, Hughton said: "The clubs are in discussion and that's one that I hope gets done."
Steve Morison could move to Elland Road as part of the Becchio switch.
Hughton added: "Whether that has to be part of the deal or not, I don't know. That's what the talks are."
Norwich remain interested in Celtic's Gary Hooper, but Hughton was uncertain if a move can be thrashed out before the closure of the transfer window on Wednesday.
"Everybody's aware where we are with him," Hughton said.
"We have put in bids for him which have been turned down by Celtic. It's their prerogative. He's a very important player for them.
"Whether anything further will happen with that one, I don't know."
A move for Kei Kamara from Major League Soccer's Sporting Kansas City is complete, subject to paperwork.
Hughton said: "From what I've seen of him, we're not just taking an average player from that division. We're taking a player from that division that has excelled in recent seasons.
"I think he'll give us another dimension in the forward area."
Norwich were much improved from Saturday's humiliating FA Cup loss to non-league Luton and the 5-0 defeat at Liverpool the previous week.
Wes Hoolahan's 32nd-minute goal gave the Canaries a deserved lead, but Spurs winger Gareth Bale equalised after 80 minutes with a scintillating run from his own half which he finished off with a shot into the bottom corner.
Tottenham manager Andre Villas-Boas described the goal as "beautiful" but was unhappy with Alex Tettey's attempt to halt Bale at the halfway line as the Welshman began his brilliant solo run.
"Had the boy got on to Gareth's ankle it's an injury that takes him out for six months," the Portuguese said.
Hughton was perplexed by Villas-Boas' reaction.
"I'm surprised by that," the Norwich boss said.
"The way that Bale went past him there didn't seem too much wrong with Gareth Bale to me. I don't think anybody got near him.
"We could pick holes in where the play started, could we have stopped it at the source? And arguably we could've done.
"Occasionally you have to hold your hand up and just say it's a great goal by a top-class player."
Tottenham, who were also knocked out of the FA Cup by lower division opposition at the weekend as Leeds won at Elland Road, had been second best in the opening half but were strong in the second and deserving of a point.
Germany international Lewis Holtby made his Spurs debut in the second period as a substitute and impressed.
Villas-Boas added: "He was good. The team improved so much in the second half that it obviously helped Lewis' performance.
"It was extremely good to see him out on the pitch. I think he had the right impact for such a short time."
The Spurs boss played down the prospect of another midfielder leaving White Hart Lane, even though Tom Huddlestone was not in the squad.
Villas-Boas said: "There was an interest from Fulham. I'm not sure if they're going to follow on that interest. He's a player we rate very highly."
Villas-Boas anticipates there will be little activity at Tottenham on the final day of the transfer window.
"It finishes tomorrow [Thursday], thankfully," he said.
"We look to be quiet in the market. It's not impossible that a couple of things happen. It's highly unlikely.
"We need to add quality to the squad and our quality to the squad is keeping the players we have now and Lewis arriving."