The Dane will name his team for Paris on Wednesday, and has four spots to fill.
Matt Wallace spectacularly won the Made In Denmark event on the weekend – his third of the season on the European Tour – under Bjorn’s watchful eye.
Wallace hasn’t previously competed in the Ryder Cup, however.
Neither have Tommy Fleetwood, Jon Rahm, Alex Noren, Tyrrell Hatton and Thorbjorn Olesen, who comprise five of the current eight-man team.
Rose has questioned whether including a sixth rookie as a wildcard would be a smart move after the experience of two years ago when USA won at a canter.
“We had five at Hazeltine and that proved too many and that is something Thomas is going to have to weigh up,” said Rose.
Ian Poulter, Henrik Stenson, Paul Casey, Rafa Cabrera-Bello and Sergio Garcia are all scrapping for one of the four wildcards.
The out of form Garcia could be vulnerable having decided against playing in Europe after missing out on the PGA Tour’s FedEx Cup play-offs.
“Sergio has not given Thomas much to work with by not playing, so we will have to wait and see,” said Rose.
US captain Jim Furyk will name three of his four picks on Tuesday with Tiger Woods, Phil Mickelson and Bryson DeChambeau favourites to be called up.