Hull FC recently announced the signing of Connor for the 2017 season, but reports have emerged that the Giants want to retain his services next year.
Hull have issued a statement reiterating that Connor is their player for next year, but Thewliss has hinted that the door remains open for Connor to stay.
“We have seen the speculation and at this stage it is just that – speculation,” he told the Huddersfield Examiner.
“When Hull made their announcement concerning Jake, we said then the door remained open for him should he wish to remain a Giant. That remains the case as far as we are concerned.
“If we receive confirmation from the RFL that Jake is registered for the 2017 season – with ourselves or any club – we will make that public.”