Spencer Downey, who represents both 21-year-olds, claims Neil Lennon wants to sign the duo, who played for St Mirren on loan last season.
Newcastle have offered a one-year extension to the pair, who are also targets for Bolton, Huddersfield and Doncaster, and whom St Mirren would like to return on loan next year.
While with the Saints, the players were in the team that won the Scottish League Cup, beating Hearts 3-2 in the final.
"They both made a massive impact up in Scotland," Downey told the Newcastle Chronicle. "St Mirren are really keen to keep them, but there has been interest from other clubs, including Celtic.
"Celtic are one of those clubs who if you do well against them, they keep an eye on you. Conor did particularly well in midfield against Victor Wanyama and Joe Ledley.
"They haven't ruled out St Mirren yet. St Mirren have shown their desire to both players."
Left-back Dummett arrived in Scotland last summer and made 36 appearances for Saints, while Newton followed in January.
The midfielder has made 19 appearances for St Mirren and scored his first goal in senior football in the 3-2 win over Hearts at Hampden Park.