Rashid has played 19 Tests for England with 60 wickets at an average of 39.83.
Rashid, England's leading tweaker in ODIs and T20Is since the 2015 World Cup, hasn't added to his 19 Test caps since January last year and not played any County Championship matches for Yorkshire in the past two seasons.
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The 32-year-old wrist-spinner signed a white-ball only contract with the club earlier this year and isn't taking part in the ongoing Bob Willis Trophy, which is a replacement for the championship curtailed by the ongoing COVID-19 pandemic for this summer.
While Rashid's 60 Test wickets have come at a cost of 39.83 apiece, the fact that no other spinner has been able to nail down the spot has kept England waiting.
Smith said he would like to see the leggie prove his long-form fitness following a shoulder injury and put himself in the reckoning once again.
"Adil's still coming back from a reasonably serious injury," he told reporters on Tuesday (August 18) after announcing England's squad for the T20Is versus Pakistan.
"He's still working on that physical side, but in the long term I think Adil still has aspirations to play for England in all forms."
With the tours to India and Sri Lanka looming large, England will want its spin reserves to be as strong as possible.
Further on Rashid, Smith said: "His form is really good in white-ball cricket. We've all seen the skill and the mastery that he's displaying at the moment in that form and we'll work closely with Adil and with Yorkshire in the future to see if he's ready to play four-day and five-day cricket."
"There is a jump required. There's a difference between bowling 10 overs and bowling 100 overs or whatever a very heavy workload would be in a two or three-game spell in four-day cricket."
"But the main thing with Adil is he's made really good strides and he's developed really well in recovery from that injury," he added.
Smith also talked about the exclusion of James Vince from the T20I squad to take on Pakistan from August 28, saying that the right-hand batsman hasn't been able to make his opportunities count.
Vince has played 13 Tests, 16 ODIs and 12 T20Is for England, but despite his talent being evident, averages below 30 in all the formats. The Hampshire right-hander now has his career hanging in the balance.
"I think James is a very talented player and at his best we all know has the skill to look absolutely at home in international cricket," said Smith.
"But I'm not saying anything different here than I said to James on the phone: it's just a question of him grabbing his opportunities. He's not been selected for this series against Pakistan. That was as far as the conversation went."
"One thing he'd be the first to say, and I think he has said it publicly, that for someone of his talent and his class he probably hasn't grabbed his opportunities in the way he would have liked to have done."
(Inputs from AFP)