Gough is due to start bowling this week and if he reaches the "right level", the chairman of selectors, David Graveney, will reassess the situation.
Gough was forced to pull out of the West Indies tour with hamstring trouble on New Year's Eve - three days before the squad were due to leave and his county colleague, Chris Silverwood, was then rushed from Kenya to replace him after initially being selected for England's A squad.
The England physiotherapist, Wayne Morton, said: "There's a very good chance of Darren joining the tour if his level of rehabilitation goes along the right lines. We are hoping he makes himself available for selection at the start of February.
"If we are satisfied that his progress is what we would wish, I am sure he has a very good chance of making the tour. "He's doing quite a bit of work - in fact he'll probably start bowling this week.
"And he'll go along similar lines as before, trying to increase his numbers of overs and his pace. He'll be under supervision at Yorkshire and we'll see how he goes. There's a fine line between being totally fit and not quite fit. I have spoken to him twice a week and he's pretty pleased with how it's going."
Should Gough satisfy all the fitness requirements, he could be available for the second Test in Port of Spain, Trinidad, on 13 February.
England play Trinidad and Tobago before the Test and that could be used as a warm-up match for the fast bowler.
Wasim Akram called for a top-level inquiry yesterday to clear his name over match-fixing and betting allegations. Wasim, who recently resigned as Pakistan captain because of the accusations, said: "I have no objection to appearing before a high-level committee because I know I am being framed by certain quarters. I have played and represented Pakistan with distinction and my conscience is crystal clear, but I want the issue to be dead once and for all and the only way to do it is to constitute a high-level commission."