Alba, 28, has not fully convinced manager Ernesto Valverde during the first half of the season, according to the report, and his declining valuation could see the player offloaded sooner rather than later.
The Spain international has enjoyed an encouraging campaign with the La Liga leaders, scoring once and contributing six assists in 18 appearances in all competitions, yet Valverde has seemingly not been impressed.
The former Valencia left-back – who last month insisted he was thrilled with life at the Nou Camp despite Neymar's shock departure to Paris Saint-Germain – is approaching the mid-way point in the new five-year deal he signed in 2015, while his €150m release clause (£132.36m) makes him unobtainable for most clubs around the world.
And Burley, who represented the likes of Chelsea and Celtic during a 15-year playing career, agrees that speculation regarding the move is fanciful.
"Playing at Barcelona, he scored a great goal against Valencia from that little pass from Messi," he told ESPN. "Why would he leave Barcelona to go to Tottenham?
"Champions League, La Liga winners and potentially again this year we'll see what happens, to go to a team who are not in the title race in England and who have got two left backs in Rose and [Ben] Davies.
"Rose could leave and though they might go for another left-back Tottenham I don't think that one is going to happen."
Speculation that Tottenham could move for a left-back has been fuelled in recent months by the uncertainty regarding the future of Rose.
The England full-back has failed to reclaim his place in the Tottenham first team since recovering from a knee injury that kept him out for 10 months, having publicly criticised the club's transfer dealings and stating his intention to leave the club.
Both he and manager Mauricio Pochettino have denied suggestions the pair have fallen out, yet Rose remains a peripheral member of the Tottenham side, making just his fifth start of the campaign in the inconsequential 3-0 Champions League win over Apoel on Wednesday (6 December).
And the 27-year-old suffered the ignominy of being withdrawn in the second half with a head injury, which Pochettino ordered Rose to have treated immediately – leading to further suggestions there had been a confrontation between the two.
But the ex-Watford loanee said, according to The Evening Standard: "This is getting silly now. The manager said it was best I came off and I didn't want to come off. That was it. I've seen that people are saying we exchanged words. There is no issue between me and the manager.
"There has never been an issue — and people trying to put stuff in the media is not welcome. For the last three-and-a-half to four years, the manager has been my biggest fan. He's given me nothing but love and respect. There is no issue. People need to stop this because it's not welcome."
Rose, from Doncaster and who started his career at Leeds United, wants to return to the north to be closer to his family and has regularly been linked with a £50m move to Manchester City and Manchester United.