The 32-year-old leg-spinner last played the most recent of his 19 Tests in January of last year and he has not featured for Yorkshire in the first-class County Championship during the past two seasons.
Earlier this year he signed a white-ball only contract with Yorkshire and so is not featuring in the Bob Willis Trophy, the replacement competition for the Championship in a season disrupted by COVID-19.
Rashid, however, was a key member of England´s World Cup-winning side last year and is their top-ranked Twenty20 bowler.
Although his 60 Test wickets have come at an expensive average of nearly 40 apiece, Smith would like to see him prove his fitness following a shoulder injury and make a challenge for a place in England´s red-ball set-up, with none of his current spin rivals having nailed down a position in Joe Root´s team.
"Adil´s still coming back from a reasonably serious injury," Smith told reporters on Tuesday after Rashid was included in England´s Twenty20 squad for an upcoming three-match series against Pakistan at Old Trafford.
"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."
Former England batsman Smith added: "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."
Meanwhile James Vince´s England career looks to be in the balance after he was omitted from the Twenty20 squad.
The Hampshire batsman has appeared more than 10 times each in the three international formats, Tests, one-day internationals and Twenty20s, but has a modest average of under 30 in all of them.
Vince failed to impress during England´s recent one-day series win over Ireland and Smith said: "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.
"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."
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