Beckford was substituted as a precaution during the interval at Hartlepool United with the visitors leading through Luciano Becchio's 23rd-minute header.
With Leeds needing to overcome a 2-1 first-leg deficit tomorrow to reach Wembley, Grayson said: "We are hopeful he will be able to play although if there is any doubt, he won't."
Grayson did not feel Beckford's withdrawal or his side's exertions in their FA Cup defeat by Spurs had contributed towards Hartlepool's unexpected fightback.
Grayson added: "Scott Flinders has made some fine saves and at 1-0 you are always vulnerable.
"It was positive to get a result after a big game on Wednesday and the players have given everything both physically and mentally."
Leeds's midfield, however, did appear to tire after a comfortable opening period. Becchio's finish from 24-goal Beckford's precise cross rewarded the visitors' dominance and the Argentine forward was only denied a hat-trick of first-half headers by fine saves from Rotherham-born Flinders. Hartlepool finally threatened after substitute Ritchie Jones's 57th-minute arrival and Casper Ankergren foiled Adam Boyd just after the hour before the home striker blasted a 71st-minute equaliser from the edge of the box.
Flinders flapped at a 78th-minute corner and Becchio poked home from close range after Richard Naylor's lob hit a post.
But the home side rallied again and Antony Sweeney headed a stoppage-time equaliser.
With neither leaders Norwich or third-placed Charlton winning, Grayson said: "We have still taken a point away from a difficult ground, and other results have gone for us."
Hartlepool United: Flinders, Austin, Collins, Liddle, Hartley, Gamble, Humphreys (Jones 57), Sweeney, Monkhouse, Larkin (Behan 46), Boyd. Unused substitutes: Cook, McSweeney, Clark, Bjornsson, Fredriksen.
Leeds United: Ankergren, Bromby, Michalik, Naylor, Lowry, Gradel, Howson, Doyle, McSheffrey (Johnson 86), Becchio, Beckford (Snodgrass 46). Unused substitutes: David Martin, Crowe, Grella, Hughes, White.
Referee: Scott Mathieson (Cheshire).
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