Naismith has scooped the young player of the year award from both the SPFA and league sponsors Bank of Scotland and Jefferies expects several enquiries over the summer.
However, the youngster was already regarded as one of the hottest properties in Scottish football this time last year and even had a trial at Arsenal but no big move materialised.
Jefferies will be thrilled if no concrete bids arrive this time around - and insists Naismith will not be too disappointed either.
He said: "If no-one comes in for him, it will just spur him on to be even better and then clubs will come in for him.
"He's still only 20 years old, you have to remember that. He's not 25 or 26, he's got bags of time in front of him and there is plenty of time for clubs to come in for him."
Rangers have already been linked with a £1million move for Naismith and could be tempted to make a move in the coming weeks after missing out on Scott Brown to rivals Celtic.
Jefferies added: "There have been no enquiries and he deals with the speculation very professionally.
"He knows if it happens, it happens. And, if it doesn't, it won't be the worst thing to be here for another year.
"He's a terrific lad to work with and that's one of his strengths. He doesn't let any of the speculation get to him or affect his form."
Celtic may have paid £4.4million for Brown but Naismith's own impressive form saw him beat the Hibernian midfielder to the Bank of Scotland award this week and Jefferies was thrilled to see the Killie man come out on top.
He said: "He won the SPFA Young Player award and it looks as though he has beaten off the same opposition to win the Bank of Scotland award.
"It's a great achievement. He's won monthly awards throughout the year and it's a fantastic season for him again. These awards have been well-earned."