This news comes after Spurs boss Mauricio Pochettino ranted about his job title and responsibilities, saying: "The club needs to change my title and description.
"Sell, buy players, sign contract, not sign the contract - I think it is not in my hands, it's in the club's hands and [chairman] Daniel Levy."
However, Pochettino may soon get his wish of new additions signed, as Levy has all but wrapped up the deal.
Patience is a virtue for Levy and Tottenham
After breaking their transfer record already once this summer with the signing of Tanguy Ndombele, it looked a certainty throughout the window that Spurs would have to do it again for Lo Celso.
However, Nabil Fekir's arrival at Real Betis means that Lo Celso has already been replaced - and funds need to be made up if they are to strengthen their side further ahead of the new season.
Reports in Spain suggest that consequently, Betis are willing to agree a lower fee than the original £70 million-plus they were after earlier in the transfer window.
Christian Eriksen and Lo Celso to line up together next season
Further reports have suggested that Christian Eriksen is set to stay at White Hart Lane for at least the first half of the season - therefore quashing earlier suggestions that Lo Celso was his replacement.
The Argentinian midfielder, 23, is supposedly very keen to work alongside his compatriot Mauricio Pochettino, who wants to build the side with both him and Eriksen in it.
Lo Celso is capable of playing in centre-midfield or further up the field, which may mean he starts alongside Ndombele or alongside Eriksen.
He managed an impressive 16 goals in all competitions for Betis last season and has recently attracted interest from S.S.C. Napoli and Atletico Madrid - although it is unlikely his head will turn from his desired move to North London now.
Spurs sending a warning to Betis
If Spurs fail to acquire Lo Celso, reports are linking them strongly with a move for Manchester United target Bruno Fernandes. United have seemingly dropped out of the race after agreeing on a deal in principle to sign Lo Celso's international teammate Paulo Dybala.
Spurs would, however, have to pay a fee upwards of £62 million if they were to land the Portuguese star.
Spurs' interest in Fernandes may be a warning shot fired to Real Betis to conclude the deal before Levy pursues other targets.