Indeed, Labrune has confirmed there was concrete Marseille interest in the pair, with his coach Michel - the man who replaced Marcelo Bielsa - saying no to the signing of Adebayor.
But Spurs' Lamela had an agreement in place with the French side, he claims, which Tottenham broke off once they could not sign his replacement.
The Marseille president is quoted as saying to Le Parisien in a printed version of their paper: "It was decided to wait for a better opportunity this winter to focus on the ambitious [signing of] Erik Lamela. We obtained an agreement from the player, his agent and the club - but at 11:30 Tottenham, unable to hire his replacement, terminated negotiations."
And, on Adebayor, he said: "I took breakfast in Milan with [Adriano] Galliani, the vice president of AC Milan. Everything was okay to enlist Matri. But he was not accepted by our coach. He also did not want Adebayor."
What does the news mean for Lamela?
The fact Adebayor is no longer wanted at Tottenham was already clear for all to see but the Lamela news confirms definitively that patience is running out with the Argentine at White Hart Lane.
But the problem with there being an agreement between the player and Marseille is that he will now know he was to be offloaded and is only being kept due to the failure to sign Saido Berahino among others.
Is that going to make Lamela play any better? It's hardly the greatest motivation in the world.