But The News understands the Blues would only consider permanent moves for the attacking duo.
Danny Cowley desperately needs attacking reinforcements this summer, with no senior players currently contracted in that department next term.
Whittaker and Joseph have been mentioned as potential options and Cowley is indeed an admirer of both players, who spent time last season on loan at Lincoln and Cheltenham respectively.
Swansea are one of the teams credited with interest in Marcus Harness, with Cowley stating it would take a significant offer for Pompey to consider selling their most bankable asset.
Pompey are aware of the potential to factor Harness into any deals for the pair, but no talks have taken place between the clubs to that extent at present.
Whittaker made 29 appearances last term, with six coming for Swansea and a further 23 arriving after his move to Sincil Bank, bagging a total eight goals in the process.
The 21-year-old moved to the Liberty Stadium for £700,000 from Derby in January of last year, and still has three years to go on his existing agreement.
Meanwhile, Joseph made a decent impression at Cheltenham this season, returning four goals from 13 starts.
The 20-year-old cost the Swans £500,000 from Wigan last year and also has three years to run on his deal.
That means both would require decent fees, but reports in Wales this month suggest boss Russell Martin is prepared to let the players leave permanently.
Cowley has been told Pompey are prepared to spend on fees to get in promising players who can be developed and improve their resale value.
Both Joseph and Whittaker fit into that category, with the Blues boss also aware he will need to invest a significant portion of his transfer budget in attacking areas this summer.