Time is running out for the Cherries to get the deal over the line, with the summer transfer window set to close earlier than usual on August 9.
The 23-year-old Colombian midfielder was given two deadlines to return to training with La Liga club Levante, but missed them both - according to the Mirror - in retaliation to the fact that Levante turned down a £24m bid from the Cherries for the midfielder's services.
A potential transfer is slightly more advanced than believed, as Lerma has already agreed personal terms with Bournemouth and the midfielder has handed in a transfer request to club officials at Levante.
Time is running out for the World Cup star to earn his dream move, as Bournemouth are said to have threatened to end their interest if Levante don't relax their stance and make it easier to let the transfer go ahead.
Lerma joined Levante two years ago, after playing for Atlético Huila in his home country, and made 25 appearances in La Liga last season as the side finished 15th.
After this, he also had a productive summer as he played in all four of Colombia's games at the World cup in Russia this summer, including a start against England in the last 16 - which saw his country eliminated after a penalty shootout.
Meanwhile, Bournemouth have signed Leganes midfielder Diego Rico on a four-year deal, subject to international clearance.
"AFC Bournemouth have completed the signing of Spanish defender Diego Rico, subject to international clearance," the club reported via their official website.
"The 25-year-old has put pen to paper on a four-year contract at Vitality Stadium and arrives from Leganes for an undisclosed fee."