Ian Bell scores 65 not out as England storm to victory at Edgbaston.
The Lancashire seamer will be assessed before fifth Test at the Oval.
David Warner is hopeful that Australia can pull off a great escape and win the third Ashes Test.
Finn takes 5-45 as England close in on taking a 2-1 series lad at Edgbaston.
England face Australia in the third Test of the Ashes series on Wednesday. Find out how to follow the match live in the UK.
Hodgson's current contract is due to expire after Euro 2016, but a good performance could see him stay on.
England paired with Scotland in Group F, while Wales are drawn alongside the Republic of Ireland.
Roy Hodgson's future hinges on England's performance in next summer's European Championship.
Teams across the world will learn who they will compete against to win a place at Russia 2018.
The 37 year old underwent further tests on 22 July ahead of third Test at Edgbaston.
Gary Ballance and Ian Bell must be the casualties from England's harrowing defeat at Lord's
England bowled out for 103 in second innings as Australia level series at 1-1.
Australia lead by 362 runs to stand on the brink of levelling the series at 1-1.
England trail by 481 runs after losing four first innings wickets as Australia take control.
Australia close on 337 for 1 as they dominate day one of the second Test at Lord's.
England captain Alastair Cook expects to name all-rounder in the team at Lord's.
England hold a 1-0 lead going into the second Ashes Test at Lord's from 16 July.
The 37 year old missed training on 14 July and could be replaced by uncapped Peter Nevill.
Australia need the highest score to win an Ashes Test to take a 1-0 series lead.
Australia trail by 166 runs after day two in Cardiff where England's bowlers toiled.
Portuguese winger pays tribute to Sir Alex Ferguson but overlooks Louis van Gaal
Root makes 33 from 24 balls after Australia take a flurry of England first innings wickets.