FRISCO, Texas -- Cowboys owner and general manager Jerry Jones said Tuesday that quarterback Dak Prescott will not go on injured reserve following surgery on his right thumb Monday.

"We want him to be a consideration for playing for us within the next four games," Jones said on 105.3 The Fan in Dallas.

The initial timeline for Prescott to return was six to eight weeks, according to sources. However, Jones said the report following the surgery was more favorable. Theoretically, Prescott could be back for the Oct. 9 game at the Rams in Week 5 if things work out well in his recovery. The original thought was he could miss seven games and return potentially Nov. 13 at the Packers, following the Cowboys' bye.

"If we thought he wasn't going to be ready to go until after four games, we would put him on IR. We're not doing that," Jones told The Fan. "We think he can come in and play, so we don't want to not have him out there practicing. We want him getting prepared and we'll see how he handles this thing, how it heals, mainly his strength, how he can grip the ball, [will determine] what his status is. That's not [being] an optimist. The proof is that we got a good surgery, got good technique and feel better about it than we did Sunday night."

Prescott had a plate inserted into the thumb Monday to stabilize the joint. The first part of Prescott's recovery is making sure the wound heals, followed by working on grip strength. With the plate, the bone should be stronger than before.

Prescott suffered the injury in the fourth quarter of the Cowboys' 19-3 loss to the Buccaneers after his hand twice hit the hand of linebacker Shaq Barrett. After a screen pass to Ezekiel Elliott, Prescott went to the sideline because he could no longer grip the ball.

Prescott would have to miss a minimum of four games if he were to be placed on injured reserve. By not going on IR, Prescott would be eligible to practice. He can rehab, condition and go through meetings to help out.

"Dak has a real chance to be back out there throwing the ball pretty quick," Jones said.

The Cowboys will add a quarterback to the practice squad at the very least, but they will go with Cooper Rush and Will Grier, who are currently on the practice squad, as the starter and backup, respectively, in Prescott's absence. Rush won his first start last season replacing an injured Prescott against the Vikings.

"Those guys know the offense well," Jones said on The Fan. "They had a lot of reps in it and consequently gives us our best shot. It's unlikely since we don't have any potential trade pending -- not pending, or in the mill -- it's unlikely you'll have a veteran quarterback that could get back in here and be ready to play as well as those guys can play even if you thought you might have a talent advantage."