Lara dislocated the little finger on his right hand in the first Test six weeks ago, but continued playing and hit a record 400 not out in the final Test in Antigua 10 days ago.
Doctors advised Lara to rest the injury for a further 10 days, ruling him out of the first one-day game in Guyana last Sunday and making him doubtful for both games in his home country of Trinidad.
However, after three days spent accepting numerous accolades for his achievements in Antigua, he joined his colleagues for training on Wednesday morning. Although he did not bat, he could now return for Saturday's second game.
"Brian is very hopeful of playing in both games," West Indies media liaison Imran Khan told reporters, adding that a final decision on his fitness would be made on Friday morning, 24 hours before the second game in the seven-match series.
Lara was expected to play in a charity golf tournament on Wednesday with players from West Indies and England, a commitment criticised by former West Indies fast bowler Colin Croft.
"It sends the wrong signal," Croft said. "Instead of resting, Lara is playing golf with former West Indies players. I really don't understand that decision."
Since his arrival in Trinidad on Monday, Lara has been applauded for his feat in Antigua, where, almost 10 years after setting the previous record of 375, he reclaimed it from Australia's Matthew Hayden, who hit 380 against Zimbabwe in October last year.
Lara was also appointed as the 'sports ambassador' for his country in a ceremony headed by the Prime Minister of Trinidad, Patrick Manning.
England lead the one-day international series 1-0 after their two-wicket victory in Guyana on Sunday.
England won the Test series 3-0 to record their first series triumph in the Caribbean since 1968.
