But the Hungarian striker will have to agree to reduced terms if he is to stay put.
A clause in the 22-year-old’s original contract was activated earlier this season to tie him to the club for an additional 12 months.
That also entitled Futacs to a pay rise.
However, following relegation and with Pompey desperate to wrestle their £10.5m wage bill under control, they are seeking to lower the striker’s salary.
That would be achieved if Futacs penned the fresh contract put in front of him by Blues boss Michael Appleton.
The only other senior Pompey player offered a deal is Kelvin Etuhu, with a two-year contract tabled.
And while Appleton is keen for Futacs to stay, he is adamant it must be on suitable terms for the club.
He said: ‘Marko has been offered a deal to stay and it is up to him.
‘It is for one year and is a different one in terms of wages to what he currently has.
‘I know he wants me to guarantee him regular football but I could never promise that to anybody.
‘Regardless, he has been offered a deal to stay and it is now his choice.
‘I want Marko to stay because what he might bring to us is something different.
‘He’s a big, strong lad. Although, to be honest, I think he did his best work as more of an impact player.
‘You never know, though. If he can get a good pre-season under his belt, who knows what the season holds for him?
‘At the end of the day, an offer has been made.
‘The deal has been put into place and it is now up to him.
‘We will see what happens. It would be great if he did sign it.’
Futacs was signed in August last year following a week-long trial.
The towering Hungarian impressed then-Pompey manager Steve Cotterill and made his debut as a substitute in the 4-3 defeat at West Ham in early September.
It was under Appleton, though, when he was given his maiden Blues start – and a 12-match run in the side – at the turn of the year.
After scoring three goals in his first five matches, Futacs was linked with Old Firm duo Rangers and Celtic during the January transfer window.
However, his form noticeably experienced a slump and he made just one more start in the final 13 games of the campaign.
Regardless, he was a regular substitute and scored after coming on against Birmingham and Doncaster, taking his scoring tally to five.
Futacs has since spoken of his desire to start more matches on a regular basis.
Meanwhile, at the weekend, the striker told the Hungarian press he would like to remain at Fratton Park.
n Stephen Henderson has completed his £600,000 move to West Ham after signing a four-year deal at Upton Park, while Erik Huseklepp has returned to Fratton Park after Birmingham turned down the option of making his loan move permanent.