Shareholder activist Trian Fund Management LP has taken big stakes in investment firms Invesco Ltd. and Janus Henderson Group PLC and plans to agitate for deal making aimed at building a rival to the biggest asset managers in the world.

Trian has accumulated 9.9% stakes in both Invesco IVZ, -1.40%   and Janus Henderson JHG, -0.55%  , with the two positions totaling roughly $900 million, people familiar with the matter said.