Givet suffered a dead-leg in last weekend's dramatic 5-3 win over Bristol City but has stepped up his involvement in training throughout the week.
Marcus Olsson is still sidelined with a hamstring injury he suffered in the same game, meaning brother Martin is expected to continue at left-back.
Nuno Gomes is poised to return to Rovers' starting line-up after coming off the bench to score his fourth goal in as many games and snatch a 2-1 victory over Barnsley in midweek.
Fellow forward Colin Kazim-Richards is unlikely to be back until after the October international break following a setback with his knee problem.
Blackburn head into the game undefeated in six matches and with 14 points to their name, while Middlesbrough have lost their three away matches so far this term.
Middlesbrough boss Tony Mowbray has no fresh injury concerns.
Boro emerged from their 4-1 mauling at Blackpool on Tuesday evening physically, if not mentally, unscathed and will head for Ewood Park with only their long-term absentees missing.
They include striker Curtis Main, who underwent surgery earlier this week to repair ruptured lateral ligaments in his knee and is expected to be out of action until the New Year.
He will join defender Rhys Williams on the long road back to fitness with the Australia international in rehabilitation following ankle surgery earlier this month.
He too will be missing for months rather than weeks, but the prognosis for hamstring victim Nicky Bailey is much better with his return expected before the end of this month.