"Barry is one of the players we want to be fit," England manager Fabio Capello said of the Manchester City man.
Capello names his 23-man squad for this summer's finals in South Africa on June 1 with England's first game against the United States in Rustenburg on 12 June.
The England boss has previously stated that he would not include any player in his final selection for the tournament if they were unfit to play in the team's Group C opener.
And the 63-year-old Italian has reiterated this point, stressing: "If he [Barry] is fit, he will come with us. If not he will stay at home."
One potential safety net Capello has at his disposal is that Fifa rules allow managers to replace any player ruled out through injury after the final squads are confirmed up to 24 hours before the first game.
I think King will play the Barry role tonight with Dawson playing alongside Rio!
Flashdean
However, the former Real Madrid and Milan coach is clearly giving Barry, who has started 19 of the 22 England matches the Italian has overseen, every chance of proving his fitness.
It was initially thought Barry had an appointment with his specialist on Tuesday to assess his recovery, but instead the 29-year-old will undergo a series of rigorous tests on the injury he picked up playing for City against Tottenham in the Premier League.
If the former Aston Villa player does not prove his fitness, Capello could turn to Villa's James Milner - recently crowned Premier League young player of the year - or Michael Carrick of Manchester United.
The England manager has also been looking into the possibility of switching to a three-centre-back system.
His thinking on the subject is likely to be illuminated by his line-up for Monday's friendly with Mexico at Wembley, where he will be without the likes of Chelsea's John Terry, Ashley Cole and Frank Lampard and Portsmouth's David James following their involvement in the FA Cup final on 15 May.
After Monday's match, the England players are due to return to Irdning in the Austrian Alps for further training before playing a final warm-up match, against Japan, on Sunday.
Source: BBC Sport
Source: BBC Sport