Tyrone county board chairman Michael Kerr says he's confident Mickey Harte's side can turnaround their form and reach the Super 8s this summer.
The Red Hands needed extra time to see off Meath in Navan last Saturday evening, after having been dethroned of their Ulster crown by Monaghan last month.
A trip to Carlow in Round 2 of the All-Ireland SFC qualifiers now beckons for Harte's men and Kerr has urged the county's supporters to come out in force in support of the team.
"Mickey Harte takes one match at a time, and I know his focus right now is on the game against Carlow on Saturday week, but I believe that a place in the Super 8s is a possibility for this Tyrone side," the chairman is quoted saying by the Belfast Telegraph.
"Nobody could ever have foreseen some of the results that popped up in Ulster and this shows that championship football can be unpredictable.
"If we do manage to get into the Super 8s it would give us three more matches on a league basis which would be a new challenge. For now, I would like to see everyone get behind the side."