But Saints boss Tommy Wright remains hopeful of getting his summer transfer business done early and Alston remains in his sights.
"Fans think you want a player and it happens overnight," he said.
"But players and agents keep their cards close to their chest and want to keep their options open."
Wright told BBC Scotland that chairman Steve Brown had agreed to increase his playing budget for next season in light of Rangers' promotion and an expected increase in competition for a top-six finish in the Scottish Premiership.
The Saints boss already has York City midfielder Michael Coulson secured on a pre-contract agreement and has also had discussions with St Mirren full-back Keith Watson and Dundee United forward Ryan Dow.
Dow's present club are in danger of being relegated form the top flight, while Alston has the chance of helping Falkirk, with whom he came through the youth ranks, win promotion to the Premiership.
Bairns manager Peter Houston remains hopeful of persuading Alston, who is out of contract this summer, to remain at Falkirk Stadium but expects to lose the midfielder.
"People like Blair Alston, we have spoken to his agent and we are waiting for them to get back to us," said Wright.
"I was down in England again this week looking at players and talking to one or two.
"I have spoken to the chairman and we feel we need to invest more in recruitment this year and that's what he is planning to do.
"Hopefully we can get some fresh faces in and help the squad maintain the standards we have set over the last few years."
St Johnstone are still waiting to hear from Blair Alston about their approach for the midfielder - three months after speaking to the 24-year-old's agent.