Despite making 27 appearances for the Reds last season, the 20-year-old has not played a single minute for his club so far this season.
Although he trained with the senior squad this week, his lack of playing time has left Boothroyd concerned, according to 'The Mirror'.
“I'm really pleased with Dom but I'm also a little bit worried about him because he is not getting the minutes and not getting the games,” Boothroyd said.
“I am happy on the pitch picking the best players, but for the good of England and for the good of British football it would be nicer if we had more players playing, certainly better for us and for them.
“Our players have proved they can do it at international level but not as many of them as there should be are getting the opportunity to do that in the Premier League.”
Solanke had the opportunity to move in the summer, with Steven Gerrard reportedly interested in taking him on loan at Rangers, but the move never came to fruition.