The Tigers have been hit by a number of injuries down the spine of the team in recent weeks but positive signs are starting to emerge.
Head of medical services Rob Price gave a comprehensive fitness update to the club's official website and gave optimistic news on the first-choice trio.
Number one goalkeeper McGregor is back in full training and deemed "available for selection" after a shoulder problem that has kept him out since the end of September.
Four-goal striker Jelavic and defender Dawson were both injured at Arsenal on October 18, the former during the warm-up and the latter in the closing stages.
They are both picking up pace in their rehabilitation and could be in contention to return against Tottenham a week on Sunday.
Price wrote: "Nikica is three-and-a-half weeks post-medial meniscectomy and he has stepped up his rehab this week
We are aiming for him to return to training next week
At this stage, his knee has reacted extremely well to rehab.
"Michael is now three-and-a-half weeks on from a lateral ankle ligament rupture and he is scheduled to return to first team training this week."
Alex Bruce is back running following a grade two hamstring injury, but question marks remain over captain Curtis Davies following a back injury suffered in the 1-0 defeat at Burnley.
"Curtis was withdrawn at Burnley last weekend with back pain
The symptoms are settling nicely although it is too early to give a full assessment," said Price.
Long-term absentee Robert Snodgrass dislocated his kneecap on the opening day of the season and is expected to be out more the majority of the season.
"He is now biking and completing strength and stability work as his knee approaches full range of movement," added Price.
Source : PA
Source: PA