The Wembley hero’s three-year deal expires at the season’s end, creating an uncertain future.
Hawkins arrived in August 2017 from Dagenaham & Redbridge for an undisclosed fee – a transfer which marked his return to the Football League.
The striker-cum-defender is among 10 members of Kenny Jackett’s first-team squad whose contracts finish in the summer of 2020.
However, Pompey’s long-held stance is not to negotiate fresh player deals, instead prioritising achieving promotion to the Championship.
An injury-hampered start to the season dictated he last month staged a latest comeback, taking his Blues tally to 90 appearances and 18 goals.
And Hawkins is comfortable with sidelining the issue of his future in favour of playing.
He said: ‘I am just going to keep playing football, trying my best, playing my best.
‘Whenever the situation comes up with contract talks or my future, then I will deal with it.
‘But at the moment I’m not thinking about that, I’m just thinking about playing games of football, staying fit and being as strong as I can.
‘Contracts are a side of football I don't like getting too involved in. I am a one game at a time sort of person, trying to stay fit.
‘Obviously, I had a difficult start to the season with injuries, my focus now is just staying fit and playing games.’
A back problem initially floored Hawkins during pre-season, followed by injury near the heel of his right foot.
That absence restricted him to just one friendly outing and, despite a return to fitness, he didn’t feature in the opening eight games of the campaign.
Then, during the second half of the Carabao Cup encounter with Southampton, Hawkins was forced off with an injury to his left foot.
Last month’s trip to Rochdale staged his latest return, which resulted in a 3-0 success for Jackett’s men.
Now he’s hoping to steer clear from further injury setbacks.
Hawkins added: ‘I did the exact same injury to each foot.
‘It’s a very strange one. With the first one, I trained a lot while it was still torn and didn’t really know about it until receiving a scan.
‘I felt the second in training, then it just went during the second half against Southampton.
‘It’s something you can carry on with, but, at the end of the day, you need to be off your feet and resting it to get better.
‘And that’s difficult because you always have to be on your feet!’