Liverpool lodged a formal offer of around £2m for Jones' services on Wednesday night, but the bid was rejected.
Roy Hodgson is keen to sign a goalkeeper to replace Diego Cavalieri as the leading alternative to established number one Pepe Reina, and having tried to sign Jones during his time at Fulham, the new Liverpool boss has renewed his pursuit of the 28-year-old.
His initial offer was turned down, primarily because Gordon Strachan is hoping to secure £3.5m for Jones' services, a high enough price to fund Speroni's purchase and still leave enough to sign targets Craig Conway and Craig Dawson.
Hearts winger Andrew Driver is also a more expensive option.
The Boro boss has already inquired about Speroni's possible availability, and while Palace are reluctant to lose the Argentinian, the fact he has entered the final year of his contract means officials at Selhurst Park have admitted that a deal could be done.
Palace will demand a fee in excess of £1m, and Boro will meet their demands provided they receive their asking price for Jones.
Speroni, who recently celebrated his 31st birthday, has made more than 200 appearances since joining Palace in a £500,000 move from Dundee in 2004.
He would leap to the top of the Boro pecking order if he was to join before the end of the month, even though Danny Coyne has been pencilled in for tomorrow's Championship opener against Ipswich with Jones suspended following his dismissal on the final day of last season.
Whether Jones is still a Middlesbrough player by tomorrow's kick off remains to be seen, as it is widely expected that Liverpool will return with an improved offer in the next 24 hours.
The Australian, who signed a long-term contract at the Riverside 18 months ago, is aware of the interest from Anfield and is understood to have expressed a desire to return to the Premier League, albeit as a number two.
The shot-stopper has enjoyed a somewhat fractious relationship with the Middlesbrough fans and, while Strachan was reluctant to comment on the specifics of his position during yesterday's scheduled press conference, his insistence that every player has their price was telling.
We've had inquiries about a few of our players this week, and an offer has been made, but nothing has happened,
said the Boro boss, who has also identified Hamilton goalkeeper Tomas Cerny as a possible alternative should talks with Speroni collapse.
(Cristiano) Ronaldo left Manchester United for £80m so no one can tell me that any player is not for sale. I think Brad will probably read the papers and know of what's being mentioned, but that's life. We all get on with it.
Jones is unlikely to be the only player leaving the Riverside before the end of the month as Strachan is stepping up his attempts to move Mido, Didier Digard and Marvin Emnes out.
Nice's renewed offer for Digard still fails to meet Boro's valuation of the French midfielder, but it is hoped a compromise can be agreed that is acceptable to all parties. Similarly, talks with Turkish side Buraspor over Mido continue to progress.
None of the exiled trio have featured in a single minute of the pre-season programme, and, as he prepares to submit a formal 25-man squad for the first half of the season, Strachan has confirmed that whatever happens before the transfer window closes, Mido, Digard and Emnes have played their final game for Boro.
I don't know what's happening with Mido that's outside my hands, he said. But we have to submit a squad of 25 now with the new rules, and Didier Digard, Marvin Emnes and Mido will not be in that squad.
They have talents, they have assets and I'm sure there are clubs out there who need those assets. But at this moment in time, we're all right with what we've got without them.
Boro will also be without Rhys Williams until the turn of the year after the midfielder's long-standing pelvic problem will rule him out for more than three months.