Bournemouth are still in advanced talks with Levante, despite having initial offers knocked back by the Spanish club.
The 23-year-old Colombian handed in a transfer request to his current club in order to try and speed up the deal.
'Sky Sports' reported that the Cherries had had a £16m bid knocked back, and that Levante were looking for a fee around £27m.
However, it is now being reported that Bournemouth have offered £25m for the player.
Lerma will now travel to England for a medical this weekend, but the transfer will still depend on personal terms being agreed as well as a work permit being granted.
It was understood that several Bundesliga teams were also interested in Lerma but were not willing to pay over £8.8m.
Lerma, who is predominantly a defensive midfielder but can also fill in at right-back made 28 appearances for Levante last season.