Lilywhites manager Antonio Conte is drawing up plans for life without current incumbent Hugo Lloris, who turns 37 in December and is out of contract at the end of next season.
Lloris's error-strewn performances this season have also drawn criticism, although the Frenchman has still been a huge miss as he recuperates from a serious knee injury.
Fraser Forster will likely deputise in goal until April, while Brandon Austin and Alfie Whiteman - the latter of whom recently signed a new deal until 2025 - are also at Conte's disposal.
However, neither Austin nor Brandon have enjoyed breakthrough seasons at the Tottenham Hotspur Stadium, and a host of shot-stoppers are being tipped to succeed Lloris from next season.
Emiliano Martinez, Mike Maignan, David Raya and Jordan Pickford have all been linked with moves to North London, although the latter has now signed a new long-term deal at Everton.
Instead, football.london claims that Henderson has now emerged as a potential candidate, with the 25-year-old widely expected to sever ties with Manchester United at the end of the season.
Following a stellar two-year stint with Sheffield United, Henderson briefly succeeded in displacing David de Gea as the Red Devils' number one, but he quickly fell back behind the Spaniard in the pecking order.
The England international subsequently joined Nottingham Forest on loan for the 2022-23 season, and he has six clean sheets to boast from 18 Premier League appearances for the Tricky Trees.
Henderson is currently sidelined with a thigh injury, leading to the marquee capture of Keylor Navas on loan from Paris Saint-Germain, but Forest are still said to be prioritising the permanent signing of Henderson this summer.
In any case, the Red Devils youth product will likely be on the way out of Old Trafford permanently this summer, having labelled the club's treatment of him "criminal" last year.
"The conversation I had, coming out of the Euro squad, was that you're coming back here to be the number one goalkeeper. I got Covid - unfortunately, no one followed through with anything they told me," Henderson told talkSPORT.
"I turned so many good loans down last summer, and they wouldn't let me go. It was frustrating. To sit there and waste 12 months is criminal really, at my age. I was fuming."
Henderson remains under contract with Man United until the summer of 2025, and he has represented their senior team on 29 occasions, keeping 13 clean sheets in the process.
Tottenham return to action with a London derby against Chelsea on Sunday, after which Man United will lock horns with Newcastle United in the EFL Cup final.