They may be the only club to come close to meeting Cole's astronomical financial demands, but there is something else - aside from Europa League football - that Liverpool can offer the free agent that Arsenal and Tottenham cannot: a guaranteed start.
It looked to be a straight shoot-out between the north London rivals for the signature of Cole, with both parties reported to have been on the verge of landing the former Chelsea midfielder at some point over the summer. Liverpool have come from nowhere, though, to offer Cole a package to keep he and his agent content because the simple truth is that they need him a lot more than Spurs or Arsenal do.
Even throughout his very public courtship of the midfielder, it always seemed as though Harry Redknapp looked upon Cole as a treat rather than an addition crucial to Tottenham's fortunes.
Redknapp's obvious preference for a front two and the presence of Luka Modric in the centre of midfield means Cole would inevitably be shifted out wide at White Hart Lane, where he would have to do battle with Niko Kranjcar, Gareth Bale and Aaron Lennon for a starting berth.
If Cole didn't fancy a fight for the shirt at Spurs, then Arsenal definitely wasn't for him. There is not a club in the world that needs Cole less than the Gunners right now.
There may be three places off Robin van Persie up for grabs in the Arsenal side, but Arsene Wenger has an embarrassment of riches in that department, with Andrey Arshavin, Samir Nasri, Thomas Rosicky, Theo Walcott, Marouane Chamakh and Jack Wilshere all at his disposal.
Would Gunners supporters put Cole in the top three of that group of players? Probably not, and nor would Wenger.
Liverpool on the other hand can justify the outlay on Cole because he is better than what they already have.
If Steven Gerrard and Fernando Torres choose to stick around at Anfield, Cole may well be stuck out on the left but he'll be cutting inside off the touchline at Anfield safe in the knowledge that he'll be back doing the same thing the following week, almost regardless of his form.
Ryan Babel and Albert Riera offer Cole virtually nothing in the way of competition, and Liverpool's willingness to offer a weekly wage of around £90,000 as well as a huge signing-on fee shows the faith Roy Hodgson clearly has in Cole. The England international never had that assurance from any of the six managers he played under in eight years at Stamford Bridge and at this stage in Cole's career, that is something he will have found just as appealing as the money.
Chelsea, it must be said, for all their lavish spending of recent years have demonstrated their new-found financial savviness in replacing Cole with Yossi Benayoun. The Blues have replaced Cole, who was clearly unhappy on the champions' bench, with a similar player of a similar age on a cheaper contract.
Many scoffed at Roman Abramovic for sanctioning a £5.5million deal for the Israeli. Benayoun, though, will be more content with the limited amount of playing time on offer under Carlo Ancelotti and the size of Cole's signing-on fee coupled with his huge wage shows why the Blues were prepared to watch the midfielder walk out of Stamford Bridge for nothing. The fact that Cole looks set to join a club that his former employers will not see as a major threat this season will only reinforce Chelsea's belief that releasing Cole was the right thing to do.
Liverpool aside, the only other club who could have matched Cole's ambition was Manchester United. To many outsiders, he appeared tailor-made for the Red Devils, but with money tight at Old Trafford and Sir Alex Ferguson looking for value as much as talent these days, Cole's demands were never likely to be met.
With so much doom and gloom around Liverpool these days, the Cole deal will be warmly greeted on Merseyside. If - and it remains a big if at this point - Torres and Gerrard do hang around, the Reds will boast one of the best sides in the Premier League, especially with the likely addition of a left-back to Hodgson's ranks. Sadly for the Anfield faithful though, the quality of the starting XI is not replicated throughout their 25-man first-team squad.
Liverpool may well beat Tottenham and Arsenal to sign this summer's most talked-about free agent, who will surely be a success if he pulls on a red shirt. But Spurs and the Gunners still look likely to join Chelsea and the two Manchester clubs in keeping Cole and his new team-mates out of the Champions League places come next May.