The 30-year-old midfielder, who has been offered a new deal at Hereford where he is club captain, is training with the Robins and will turn out for them against Bishop's Cleeve on Friday.
"From a personal point of view it would be ideal, so we will see what happens over the next few weeks," Smith told the Citizen.
"I live in Worcester so it's only 25 minutes down the road. The manager (Martin Allen) invited me to train and we will have a look at things, see how it goes and have a chat as pre-season goes on.
"Whether I sign for Cheltenham or not, it's good for me as I need to be training and keeping myself ticking over."
The former Weymouth man does not see himself returning to Hereford, though, and added: "Unless they come back to me with another offer, which I don't envisage happening now, it's probably time for me to move and look somewhere else."