The on-loan Norwich City forward is out of contract at Carrow Road in the summer, and initially joined Hearts in January last year.
The Gorgie side are keen to hang onto the former Kilmarnock, Rangers and Everton striker and the 32-year-old has said he has thought about extending his stay in the Capital.
“It’s something I’ve thought about. Hopefully I can come to a conclusion sooner rather than later”, he told the BBC.
“The opportunity Hearts have given me over the last 18 months has been great. I’ve enjoyed every minute of it and the relationship I have with the manager and the way we have chatted - it is definitely a really appealing option for me.
“When, as a family, I know exactly what I want to do, we’ll move forward rather than let it drag on.”
Naismith has scored 16 goals for Hearts this season - despite missing a chunk of games in the first half of the campaign through injury - but is currently out injured having undergone knee surgery earlier this month.
Hearts boss Craig Levein is hopeful that the Scotland international can return to action before the season is out but the 49-times capped forward is exercising caution.
“I’m not going to say I’ll definitely be back [before the end of the season] but all round, it was better than expected. When you go in for an operation, they are normally saying it was slightly worse but this was better.
“It’s a rapid incline once you’ve passed the first hurdle”, he added.
He is unlikely to line up against Inverness Caledonian Thistle in the Scottish Cup semi-final next month, and will also miss Scotland’s Euro 2020 qualifying matches against Kazakhstan and San Marino.
However, Naismith remains hopeful of breaking the 50-cap mark and entering the Hall of Fame.
“As a kid, I never really expected to get any caps so to be flirting with the prospect of getting in the Hall of Fame is quite incredible. I’ll hopefully get there one day,” he told BBC Sportsound.
“When you are a kid and you go with your boys club to Hampden to watch Scotland, you are sitting there with it being a show. I never had a real thought of thinking ‘I’ll play for Scotland’.”