A report in Italy's La Gazzetta dello Sport says that the Welshman could back up his 2018 Tour victory in Italy.
"An official decision will be made in the next days," it said.
The decision could come by January 24, when Thomas is due to visit Italy's Piedmont region for an event related to the race.
Team Sky did not comment on Thomas's participation when asked.
Thomas already explained that it could be the "wrong time" for the Giro because he wants to return to the Tour de France with the number one on his back as defending champion. He won the Tour last July with the support of Team Sky and Chris Froome, who started as the team's leader.
"I definitely feel there's unfinished business there [Giro] but next year might be the wrong time," Thomas told BBC Wales in December.
"Being there [at the Tour] with number one on my back, it would be a shame to know I wouldn't be at my best, so I'm definitely leaning more towards that."
If he does race he would join Vincenzo Nibali (Bahrain-Merida) and Tom Dumoulin (Sunweb) who are planning to race both Grand Tours in Italy and France in 2019. Dumoulin placed second in both the Giro and Tour in 2018, first behind Froome and then behind Thomas. He said that he decided on focusing on the Giro first in 2019 because the route with its three individual time trials suits him.
The 2019 Giro route includes 58.5 kilometres of individual time trials over three stages. It starts with an uphill in Bologna, includes a longer rolling uphill one to San Marino mid-race and concludes outside of Verona's famous arena with 15.6 kilometres.
The time trials and usual mix of mountains would of course suit Thomas. He won the two main Alpine stages in the Tour last year and cemented his victory in the final time trail.
Organiser RCS Sport already has plenty of stars planning on racing in 2019 with Nibali, Dumoulin, Simon Yates (Mitchelton-Scott), Mikel Landa (Movistar), Alejandro Valverde (Movistar) and Primož Roglič (Jumbo-Visma).
Team Sky announced earlier it is sending Egan Bernal and Gianni Moscon. Thomas would in theory captain the team with the duo as plan B.
The Thomas coup should not come as a surprise considering RCS Sport's ability sway stars to their race in the past: Froome in 2018, Nairo Quintana and Thomas in 2017, and Bradley Wiggins in 2013.
Thomas raced the Giro for a third time in 2017 as co-captain with then team-mate Mikel Landa. They both crashed due to a parked police motorbike in the Blockhaus stage. Thomas, despite placing second to Dumoulin in the long time trial, had to abandon with shoulder and knee pain.
Thank you for reading 10 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1