In Jesus' time, Fr. Keating says, nobody had a house with more than one room in it - if indeed they had a house at all. So Jesus is really using the image of the private room to say ‘When you seek God, go into your innermost level.'
A number of Psalms point to the silence of resting in God. Here is part of psalm 131:
"But I have stilled and quieted my soul;
like a weaned child with its mother,
like a weaned child is my soul within me."