Graveney, accompanied by a fellow selector, Mike Gatting, was at The Oval to see Stewart make his return to first-class cricket for Surrey, the championship leaders, against Lancashire.
Graveney said: "There are lots of Test players on view here and, while we recognise the importance of the England captaincy, we are unlikely to be making any announcement until after the World Cup."
Surrey's 98 for 2 off 28 overs left them in a strong position after Lancashire's 194 all out. Mike Atherton, also making a return to first- class cricket following the back trouble which kept him out of the World Cup, looked in good touch until he was dismissed for 24 after 188 minutes by the novice left-arm spinner, Rupesh Amin.
When Mark Butcher was out for 40, Stewart came to the crease with Surrey 71 for 1. He survived lbw appeals on his first two balls, from Andrew Flintoff, but finished on 22 not out.
The one player who looked on course for a place in the England Test side was Alex Tudor, the Surrey fast bowler, who took 4 for 60 from his 20 overs to take his season's tally to 34.
Ben Smith, Leicestershire's acting captain, helped his side take control of their match with second-placed Hampshire with his first century of the season at Southampton. Smith made an unbeaten 126 as Leicestershire reached 327 for 6.
Worcestershire picked up only their second batting bonus point of the season by crawling to 226 for eight off 104 overs on the opening day against Somerset at New Road. Their acting captain, Graeme Hick, scored 50.Reuse content